Sr Examen

Otras calculadoras

x*((x+1)^2*(x+2)^3*(x+3)^4)/((x+4)^2*(x+5)^3*(2x+7)^5)exp(-x)
Derivada de la función/ x*((x+1)^2*(x+2)^3*(x+3)^4)/((x+4)^2*(x+5)^3*(2x+7)^5)exp(-x)

Derivada de x*((x+1)^2*(x+2)^3*(x+3)^4)/((x+4)^2*(x+5)^3*(2x+7)^5)exp(-x)

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
         2        3        4    
x*(x + 1) *(x + 2) *(x + 3)   -x
----------------------------*e  
       2        3          5    
(x + 4) *(x + 5) *(2*x + 7)
x(x+1)2(x+2)3(x+3)4(x+4)2(x+5)3(2x+7)5e−x\frac{x \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{4}}{\left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5}} e^{- x} 
((x*(((x + 1)^2*(x + 2)^3)*(x + 3)^4))/((((x + 4)^2*(x + 5)^3)*(2*x + 7)^5)))*exp(-x)
Solución detallada

  1. Se aplica la regla de la derivada parcial:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}

    f(x)=x(x+1)2(x+2)3(x+3)4f{\left(x \right)} = x \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{4} y g(x)=(x+4)2(x+5)3(2x+7)5exg{\left(x \right)} = \left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5} e^{x}.

    Para calcular ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Se aplica la regla de la derivada de una multiplicación:

      ddxf0⁡(x)f1⁡(x)f2⁡(x)f3⁡(x)=f0⁡(x)f1⁡(x)f2⁡(x)ddxf3⁡(x)+f0⁡(x)f1⁡(x)f3⁡(x)ddxf2⁡(x)+f0⁡(x)f2⁡(x)f3⁡(x)ddxf1⁡(x)+f1⁡(x)f2⁡(x)f3⁡(x)ddxf0⁡(x)\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} = \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{3}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{2}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{1}}{\left(x \right)} + \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}

      f0⁡(x)=x\operatorname{f_{0}}{\left(x \right)} = x; calculamos ddxf0⁡(x)\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}:

      1. Según el principio, aplicamos: xx tenemos 11

      f1⁡(x)=(x+1)2\operatorname{f_{1}}{\left(x \right)} = \left(x + 1\right)^{2}; calculamos ddxf1⁡(x)\frac{d}{d x} \operatorname{f_{1}}{\left(x \right)}:

      1. Sustituimos u=x+1u = x + 1.

      2. Según el principio, aplicamos: u2u^{2} tenemos 2u2 u

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(x+1)\frac{d}{d x} \left(x + 1\right):

        1. diferenciamos x+1x + 1 miembro por miembro:

          1. La derivada de una constante 11 es igual a cero.

          2. Según el principio, aplicamos: xx tenemos 11

          Como resultado de: 11

        Como resultado de la secuencia de reglas:

        2x+22 x + 2

      f2⁡(x)=(x+2)3\operatorname{f_{2}}{\left(x \right)} = \left(x + 2\right)^{3}; calculamos ddxf2⁡(x)\frac{d}{d x} \operatorname{f_{2}}{\left(x \right)}:

      1. Sustituimos u=x+2u = x + 2.

      2. Según el principio, aplicamos: u3u^{3} tenemos 3u23 u^{2}

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(x+2)\frac{d}{d x} \left(x + 2\right):

        1. diferenciamos x+2x + 2 miembro por miembro:

          1. La derivada de una constante 22 es igual a cero.

          2. Según el principio, aplicamos: xx tenemos 11

          Como resultado de: 11

        Como resultado de la secuencia de reglas:

        3(x+2)23 \left(x + 2\right)^{2}

      f3⁡(x)=(x+3)4\operatorname{f_{3}}{\left(x \right)} = \left(x + 3\right)^{4}; calculamos ddxf3⁡(x)\frac{d}{d x} \operatorname{f_{3}}{\left(x \right)}:

      1. Sustituimos u=x+3u = x + 3.

      2. Según el principio, aplicamos: u4u^{4} tenemos 4u34 u^{3}

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(x+3)\frac{d}{d x} \left(x + 3\right):

        1. diferenciamos x+3x + 3 miembro por miembro:

          1. La derivada de una constante 33 es igual a cero.

          2. Según el principio, aplicamos: xx tenemos 11

          Como resultado de: 11

        Como resultado de la secuencia de reglas:

        4(x+3)34 \left(x + 3\right)^{3}

      Como resultado de: 4x(x+1)2(x+2)3(x+3)3+3x(x+1)2(x+2)2(x+3)4+x(x+2)3(x+3)4(2x+2)+(x+1)2(x+2)3(x+3)44 x \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{3} + 3 x \left(x + 1\right)^{2} \left(x + 2\right)^{2} \left(x + 3\right)^{4} + x \left(x + 2\right)^{3} \left(x + 3\right)^{4} \left(2 x + 2\right) + \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{4}

    Para calcular ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Se aplica la regla de la derivada de una multiplicación:

      ddxf0⁡(x)f1⁡(x)f2⁡(x)f3⁡(x)=f0⁡(x)f1⁡(x)f2⁡(x)ddxf3⁡(x)+f0⁡(x)f1⁡(x)f3⁡(x)ddxf2⁡(x)+f0⁡(x)f2⁡(x)f3⁡(x)ddxf1⁡(x)+f1⁡(x)f2⁡(x)f3⁡(x)ddxf0⁡(x)\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} = \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{3}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{2}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{1}}{\left(x \right)} + \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}

      f0⁡(x)=(x+4)2\operatorname{f_{0}}{\left(x \right)} = \left(x + 4\right)^{2}; calculamos ddxf0⁡(x)\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}:

      1. Sustituimos u=x+4u = x + 4.

      2. Según el principio, aplicamos: u2u^{2} tenemos 2u2 u

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(x+4)\frac{d}{d x} \left(x + 4\right):

        1. diferenciamos x+4x + 4 miembro por miembro:

          1. La derivada de una constante 44 es igual a cero.

          2. Según el principio, aplicamos: xx tenemos 11

          Como resultado de: 11

        Como resultado de la secuencia de reglas:

        2x+82 x + 8

      f1⁡(x)=(x+5)3\operatorname{f_{1}}{\left(x \right)} = \left(x + 5\right)^{3}; calculamos ddxf1⁡(x)\frac{d}{d x} \operatorname{f_{1}}{\left(x \right)}:

      1. Sustituimos u=x+5u = x + 5.

      2. Según el principio, aplicamos: u3u^{3} tenemos 3u23 u^{2}

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(x+5)\frac{d}{d x} \left(x + 5\right):

        1. diferenciamos x+5x + 5 miembro por miembro:

          1. La derivada de una constante 55 es igual a cero.

          2. Según el principio, aplicamos: xx tenemos 11

          Como resultado de: 11

        Como resultado de la secuencia de reglas:

        3(x+5)23 \left(x + 5\right)^{2}

      f2⁡(x)=(2x+7)5\operatorname{f_{2}}{\left(x \right)} = \left(2 x + 7\right)^{5}; calculamos ddxf2⁡(x)\frac{d}{d x} \operatorname{f_{2}}{\left(x \right)}:

      1. Sustituimos u=2x+7u = 2 x + 7.

      2. Según el principio, aplicamos: u5u^{5} tenemos 5u45 u^{4}

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(2x+7)\frac{d}{d x} \left(2 x + 7\right):

        1. diferenciamos 2x+72 x + 7 miembro por miembro:

          1. La derivada de una constante 77 es igual a cero.

          2. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.

            1. Según el principio, aplicamos: xx tenemos 11

            Entonces, como resultado: 22

          Como resultado de: 22

        Como resultado de la secuencia de reglas:

        10(2x+7)410 \left(2 x + 7\right)^{4}

      f3⁡(x)=ex\operatorname{f_{3}}{\left(x \right)} = e^{x}; calculamos ddxf3⁡(x)\frac{d}{d x} \operatorname{f_{3}}{\left(x \right)}:

      1. Derivado exe^{x} es.

      Como resultado de: (x+4)2(x+5)3(2x+7)5ex+10(x+4)2(x+5)3(2x+7)4ex+3(x+4)2(x+5)2(2x+7)5ex+(x+5)3(2x+7)5(2x+8)ex\left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5} e^{x} + 10 \left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{4} e^{x} + 3 \left(x + 4\right)^{2} \left(x + 5\right)^{2} \left(2 x + 7\right)^{5} e^{x} + \left(x + 5\right)^{3} \left(2 x + 7\right)^{5} \left(2 x + 8\right) e^{x}

    Ahora aplicamos la regla de la derivada de una divesión:

    (−x(x+1)2(x+2)3(x+3)4((x+4)2(x+5)3(2x+7)5ex+10(x+4)2(x+5)3(2x+7)4ex+3(x+4)2(x+5)2(2x+7)5ex+(x+5)3(2x+7)5(2x+8)ex)+(x+4)2(x+5)3(2x+7)5(4x(x+1)2(x+2)3(x+3)3+3x(x+1)2(x+2)2(x+3)4+x(x+2)3(x+3)4(2x+2)+(x+1)2(x+2)3(x+3)4)ex)e−2x(x+4)4(x+5)6(2x+7)10\frac{\left(- x \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{4} \left(\left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5} e^{x} + 10 \left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{4} e^{x} + 3 \left(x + 4\right)^{2} \left(x + 5\right)^{2} \left(2 x + 7\right)^{5} e^{x} + \left(x + 5\right)^{3} \left(2 x + 7\right)^{5} \left(2 x + 8\right) e^{x}\right) + \left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5} \left(4 x \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{3} + 3 x \left(x + 1\right)^{2} \left(x + 2\right)^{2} \left(x + 3\right)^{4} + x \left(x + 2\right)^{3} \left(x + 3\right)^{4} \left(2 x + 2\right) + \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{4}\right) e^{x}\right) e^{- 2 x}}{\left(x + 4\right)^{4} \left(x + 5\right)^{6} \left(2 x + 7\right)^{10}}

  2. Simplificamos:

    (−2x13−65x12−912x11−7235x10−35316x9−105411x8−160246x7+61331x6+863130x5+1969460x4+2400762x3+1682208x2+623592x+90720)e−x64x13+3392x12+82800x11+1232608x10+12485276x9+90870804x8+488932137x7+1969144200x6+5936402178x5+13231328096x4+21193220545x3+23102181900x2+15361598000x+4705960000\frac{\left(- 2 x^{13} - 65 x^{12} - 912 x^{11} - 7235 x^{10} - 35316 x^{9} - 105411 x^{8} - 160246 x^{7} + 61331 x^{6} + 863130 x^{5} + 1969460 x^{4} + 2400762 x^{3} + 1682208 x^{2} + 623592 x + 90720\right) e^{- x}}{64 x^{13} + 3392 x^{12} + 82800 x^{11} + 1232608 x^{10} + 12485276 x^{9} + 90870804 x^{8} + 488932137 x^{7} + 1969144200 x^{6} + 5936402178 x^{5} + 13231328096 x^{4} + 21193220545 x^{3} + 23102181900 x^{2} + 15361598000 x + 4705960000}

Respuesta:

(−2x13−65x12−912x11−7235x10−35316x9−105411x8−160246x7+61331x6+863130x5+1969460x4+2400762x3+1682208x2+623592x+90720)e−x64x13+3392x12+82800x11+1232608x10+12485276x9+90870804x8+488932137x7+1969144200x6+5936402178x5+13231328096x4+21193220545x3+23102181900x2+15361598000x+4705960000\frac{\left(- 2 x^{13} - 65 x^{12} - 912 x^{11} - 7235 x^{10} - 35316 x^{9} - 105411 x^{8} - 160246 x^{7} + 61331 x^{6} + 863130 x^{5} + 1969460 x^{4} + 2400762 x^{3} + 1682208 x^{2} + 623592 x + 90720\right) e^{- x}}{64 x^{13} + 3392 x^{12} + 82800 x^{11} + 1232608 x^{10} + 12485276 x^{9} + 90870804 x^{8} + 488932137 x^{7} + 1969144200 x^{6} + 5936402178 x^{5} + 13231328096 x^{4} + 21193220545 x^{3} + 23102181900 x^{2} + 15361598000 x + 4705960000}

Gráfica
02468-8-6-4-2-1010-5000000000050000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/                                                                                                                                                              2        3        4 /           5 /       3                      2        2\             2        3          4\\                                                                    
|             1               /  /       4 /       3                      2        2\            2        3        3\          2        3        4\   x*(x + 1) *(x + 2) *(x + 3) *\- (2*x + 7) *\(x + 5) *(8 + 2*x) + 3*(x + 4) *(x + 5) / - 10*(x + 4) *(x + 5) *(2*x + 7) /|  -x            2        3        4              1                -x
|----------------------------*\x*\(x + 3) *\(x + 2) *(2 + 2*x) + 3*(x + 1) *(x + 2) / + 4*(x + 1) *(x + 2) *(x + 3) / + (x + 1) *(x + 2) *(x + 3) / + ------------------------------------------------------------------------------------------------------------------------|*e   - x*(x + 1) *(x + 2) *(x + 3) *----------------------------*e  
|       2        3          5                                                                                                                                                                             4        6          10                                              |                                           2        3          5    
\(x + 4) *(x + 5) *(2*x + 7)                                                                                                                                                                       (x + 4) *(x + 5) *(2*x + 7)                                                /                                    (x + 4) *(x + 5) *(2*x + 7)
−x1(x+4)2(x+5)3(2x+7)5(x+1)2(x+2)3(x+3)4e−x+(x(x+1)2(x+2)3(x+3)4(−10(x+4)2(x+5)3(2x+7)4−(2x+7)5(3(x+4)2(x+5)2+(x+5)3(2x+8)))(x+4)4(x+5)6(2x+7)10+1(x+4)2(x+5)3(2x+7)5(x(4(x+1)2(x+2)3(x+3)3+(x+3)4(3(x+1)2(x+2)2+(x+2)3(2x+2)))+(x+1)2(x+2)3(x+3)4))e−x- x \frac{1}{\left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5}} \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{4} e^{- x} + \left(\frac{x \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{4} \left(- 10 \left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{4} - \left(2 x + 7\right)^{5} \left(3 \left(x + 4\right)^{2} \left(x + 5\right)^{2} + \left(x + 5\right)^{3} \left(2 x + 8\right)\right)\right)}{\left(x + 4\right)^{4} \left(x + 5\right)^{6} \left(2 x + 7\right)^{10}} + \frac{1}{\left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5}} \left(x \left(4 \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{3} + \left(x + 3\right)^{4} \left(3 \left(x + 1\right)^{2} \left(x + 2\right)^{2} + \left(x + 2\right)^{3} \left(2 x + 2\right)\right)\right) + \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{4}\right)\right) e^{- x}
Simplificar
Segunda derivada [src] 
                 /                                                                                                                                                                                                                                                                                                                                                                                                                                     /                                                                                                                                                                                                                           /         2 /       2            2                    \             2        2             2                               2                                                           \\                                                                                                                                              \    
                 |                                                                                                                                                                                                                                                                                                                                                                                                                 2        2        2 |                                            /  2       3        10  \   2*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   3*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   10*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   2*\(7 + 2*x) *\(5 + x)  + 3*(4 + x)  + 6*(4 + x)*(5 + x)/ + 40*(4 + x) *(5 + x)  + 10*(5 + x) *(4 + x)*(7 + 2*x) + 15*(4 + x) *(5 + x)*(7 + 2*x) + 5*(4 + x)*(5 + x)*(7 + 2*x)*(22 + 5*x)/|                                                                                                                                              |    
                 |                                                                                                                                                                                                                                                                                                                                                                                                        x*(1 + x) *(2 + x) *(3 + x) *|((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))*|----- + ----- + -------| + --------------------------------------------- + --------------------------------------------- + ---------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|                                                                                                                                              |    
       2         |    /       2 /       2            2                    \            2        2                                      \            2        2                    2        2        2            2                                                       /                                                                       x*(1 + x)*(2 + x)*(3 + x)*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))\                                \                                            \4 + x   5 + x   7 + 2*x/                       4 + x                                           5 + x                                          7 + 2*x                                                                                                       (4 + x)*(5 + x)*(7 + 2*x)                                                                                 /   2*(1 + x)*(2 + x)*(3 + x)*(x*((3 + x)*(7 + 5*x) + 4*(1 + x)*(2 + x)) + (1 + x)*(2 + x)*(3 + x))*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))|  -x
(3 + x) *(2 + x)*|2*x*\(3 + x) *\(2 + x)  + 3*(1 + x)  + 6*(1 + x)*(2 + x)/ + 6*(1 + x) *(2 + x)  + 4*(1 + x)*(2 + x)*(3 + x)*(7 + 5*x)/ + 8*(1 + x) *(2 + x) *(3 + x) + x*(1 + x) *(2 + x) *(3 + x)  + 2*(3 + x) *(1 + x)*(2 + x)*(7 + 5*x) + 2*(1 + x)*(2 + x)*(3 + x)*|-x*((3 + x)*(7 + 5*x) + 4*(1 + x)*(2 + x)) - (1 + x)*(2 + x)*(3 + x) + ---------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------|*e  
                 \                                                                                                                                                                                                                                                       \                                                                                             (4 + x)*(5 + x)*(7 + 2*x)                      /                                                                                                                                                                                                               (4 + x)*(5 + x)*(7 + 2*x)                                                                                                                                                                                                                                                                         (4 + x)*(5 + x)*(7 + 2*x)                                                         /    
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         2        3          5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  (4 + x) *(5 + x) *(7 + 2*x)
(x+2)(x+3)2(x(x+1)2(x+2)2(x+3)2+x(x+1)2(x+2)2(x+3)2((10(x+4)(x+5)+(2x+7)(5x+22))(102x+7+3x+5+2x+4)+10(10(x+4)(x+5)+(2x+7)(5x+22))2x+7+3(10(x+4)(x+5)+(2x+7)(5x+22))x+5+2(10(x+4)(x+5)+(2x+7)(5x+22))x+4−2(40(x+4)2(x+5)2+15(x+4)2(x+5)(2x+7)+10(x+4)(x+5)2(2x+7)+5(x+4)(x+5)(2x+7)(5x+22)+(2x+7)2(3(x+4)2+6(x+4)(x+5)+(x+5)2))(x+4)(x+5)(2x+7))(x+4)(x+5)(2x+7)+2x(6(x+1)2(x+2)2+4(x+1)(x+2)(x+3)(5x+7)+(x+3)2(3(x+1)2+6(x+1)(x+2)+(x+2)2))+8(x+1)2(x+2)2(x+3)+2(x+1)(x+2)(x+3)2(5x+7)+2(x+1)(x+2)(x+3)(x(x+1)(x+2)(x+3)(10(x+4)(x+5)+(2x+7)(5x+22))(x+4)(x+5)(2x+7)−x(4(x+1)(x+2)+(x+3)(5x+7))−(x+1)(x+2)(x+3))−2(x+1)(x+2)(x+3)(x(4(x+1)(x+2)+(x+3)(5x+7))+(x+1)(x+2)(x+3))(10(x+4)(x+5)+(2x+7)(5x+22))(x+4)(x+5)(2x+7))e−x(x+4)2(x+5)3(2x+7)5\frac{\left(x + 2\right) \left(x + 3\right)^{2} \left(x \left(x + 1\right)^{2} \left(x + 2\right)^{2} \left(x + 3\right)^{2} + \frac{x \left(x + 1\right)^{2} \left(x + 2\right)^{2} \left(x + 3\right)^{2} \left(\left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right) \left(\frac{10}{2 x + 7} + \frac{3}{x + 5} + \frac{2}{x + 4}\right) + \frac{10 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{2 x + 7} + \frac{3 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{x + 5} + \frac{2 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{x + 4} - \frac{2 \left(40 \left(x + 4\right)^{2} \left(x + 5\right)^{2} + 15 \left(x + 4\right)^{2} \left(x + 5\right) \left(2 x + 7\right) + 10 \left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right) + 5 \left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right) \left(5 x + 22\right) + \left(2 x + 7\right)^{2} \left(3 \left(x + 4\right)^{2} + 6 \left(x + 4\right) \left(x + 5\right) + \left(x + 5\right)^{2}\right)\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)}\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)} + 2 x \left(6 \left(x + 1\right)^{2} \left(x + 2\right)^{2} + 4 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(5 x + 7\right) + \left(x + 3\right)^{2} \left(3 \left(x + 1\right)^{2} + 6 \left(x + 1\right) \left(x + 2\right) + \left(x + 2\right)^{2}\right)\right) + 8 \left(x + 1\right)^{2} \left(x + 2\right)^{2} \left(x + 3\right) + 2 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right)^{2} \left(5 x + 7\right) + 2 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(\frac{x \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)} - x \left(4 \left(x + 1\right) \left(x + 2\right) + \left(x + 3\right) \left(5 x + 7\right)\right) - \left(x + 1\right) \left(x + 2\right) \left(x + 3\right)\right) - \frac{2 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(x \left(4 \left(x + 1\right) \left(x + 2\right) + \left(x + 3\right) \left(5 x + 7\right)\right) + \left(x + 1\right) \left(x + 2\right) \left(x + 3\right)\right) \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)}\right) e^{- x}}{\left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5}}
Simplificar
Tercera derivada [src] 
        /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          /                                                                                                                                                                                                                                                                                                                                               /  2       3        10  \                                                 /  2       3        10  \                                                  /  2       3        10  \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       /  2       3        10  \ /         2 /       2            2                    \             2        2             2                               2                                                           \\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          \    
        |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |                                                                                                                                                                                                                                                                                                 2*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))*|----- + ----- + -------|   3*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))*|----- + ----- + -------|   10*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))*|----- + ----- + -------|                                                                                                                                                          /         2 /       2            2                    \             2        2             2                               2                                                           \      /         2 /       2            2                    \             2        2             2                               2                                                           \      /         2 /       2            2                    \             2        2             2                               2                                                           \     /           3 /       2            2                    \             3          2              2        3               2         /       2            2                    \             2          2                     2          2                      3                                2        2                       2                             \   2*|----- + ----- + -------|*\(7 + 2*x) *\(5 + x)  + 3*(4 + x)  + 6*(4 + x)*(5 + x)/ + 40*(4 + x) *(5 + x)  + 10*(5 + x) *(4 + x)*(7 + 2*x) + 15*(4 + x) *(5 + x)*(7 + 2*x) + 5*(4 + x)*(5 + x)*(7 + 2*x)*(22 + 5*x)/|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |    
        |                                                                                                                                                                                                             /                                                                                                                                                                                                                           /                                                                                                                                                                                                                           /         2 /       2            2                    \             2        2             2                               2                                                           \\                                                                                                                                              \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         2        3        3 |                                              /   3          6           60              6                  20                  30       \   10*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   21*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   220*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))                                                 \4 + x   5 + x   7 + 2*x/                                                 \4 + x   5 + x   7 + 2*x/                                                  \4 + x   5 + x   7 + 2*x/   24*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   80*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   120*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   60*\(7 + 2*x) *\(5 + x)  + 3*(4 + x)  + 6*(4 + x)*(5 + x)/ + 40*(4 + x) *(5 + x)  + 10*(5 + x) *(4 + x)*(7 + 2*x) + 15*(4 + x) *(5 + x)*(7 + 2*x) + 5*(4 + x)*(5 + x)*(7 + 2*x)*(22 + 5*x)/   18*\(7 + 2*x) *\(5 + x)  + 3*(4 + x)  + 6*(4 + x)*(5 + x)/ + 40*(4 + x) *(5 + x)  + 10*(5 + x) *(4 + x)*(7 + 2*x) + 15*(4 + x) *(5 + x)*(7 + 2*x) + 5*(4 + x)*(5 + x)*(7 + 2*x)*(22 + 5*x)/   12*\(7 + 2*x) *\(5 + x)  + 3*(4 + x)  + 6*(4 + x)*(5 + x)/ + 40*(4 + x) *(5 + x)  + 10*(5 + x) *(4 + x)*(7 + 2*x) + 15*(4 + x) *(5 + x)*(7 + 2*x) + 5*(4 + x)*(5 + x)*(7 + 2*x)*(22 + 5*x)/   2*\3*(7 + 2*x) *\(4 + x)  + 3*(5 + x)  + 6*(4 + x)*(5 + x)/ + 10*(5 + x) *(7 + 2*x)  + 240*(4 + x) *(5 + x)  + 20*(7 + 2*x) *(5 + x)*\(5 + x)  + 3*(4 + x)  + 6*(4 + x)*(5 + x)/ + 30*(4 + x) *(7 + 2*x) *(5 + x) + 60*(5 + x) *(7 + 2*x) *(4 + x) + 160*(5 + x) *(4 + x)*(7 + 2*x) + 240*(4 + x) *(5 + x) *(7 + 2*x) + 40*(5 + x) *(4 + x)*(7 + 2*x)*(22 + 5*x)/     \4 + x   5 + x   7 + 2*x/                                                                                                                                                                                         |                                                                                                     /                                                                                                                                                                                                                           /         2 /       2            2                    \             2        2             2                               2                                                           \\|    
        |                                                                                                                                                                                                             |                                                                                                                                                                                                       2        2        2 |                                            /  2       3        10  \   2*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   3*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   10*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   2*\(7 + 2*x) *\(5 + x)  + 3*(4 + x)  + 6*(4 + x)*(5 + x)/ + 40*(4 + x) *(5 + x)  + 10*(5 + x) *(4 + x)*(7 + 2*x) + 15*(4 + x) *(5 + x)*(7 + 2*x) + 5*(4 + x)*(5 + x)*(7 + 2*x)*(22 + 5*x)/|                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                x*(1 + x) *(2 + x) *(3 + x) *|2*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))*|-------- + -------- + ---------- + --------------- + ----------------- + -----------------| + ---------------------------------------------- + ---------------------------------------------- + ----------------------------------------------- + ----------------------------------------------------------------------- + ----------------------------------------------------------------------- + ------------------------------------------------------------------------ + ---------------------------------------------- + ---------------------------------------------- + ----------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|            2        2                                                                               |                                            /  2       3        10  \   2*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   3*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   10*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))   2*\(7 + 2*x) *\(5 + x)  + 3*(4 + x)  + 6*(4 + x)*(5 + x)/ + 40*(4 + x) *(5 + x)  + 10*(5 + x) *(4 + x)*(7 + 2*x) + 15*(4 + x) *(5 + x)*(7 + 2*x) + 5*(4 + x)*(5 + x)*(7 + 2*x)*(22 + 5*x)/||    
        |                                                                                                                                                                                                             |                                                                                                                                                                                              x*(1 + x) *(2 + x) *(3 + x) *|((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))*|----- + ----- + -------| + --------------------------------------------- + --------------------------------------------- + ---------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                                                                                                    /  /       2 /       2            2                    \            2        2                                      \            2        2                  2                          \                                |                                              |       2          2            2   (4 + x)*(5 + x)   (4 + x)*(7 + 2*x)   (5 + x)*(7 + 2*x)|                             2                                                2                                                  2                                                      4 + x                                                                     5 + x                                                                    7 + 2*x                                                   (4 + x)*(5 + x)                                 (4 + x)*(7 + 2*x)                                 (5 + x)*(7 + 2*x)                                                                                                                            2                                                                                                                                                                                   2                                                                                                                                                                                     2                                                                                                                                                                                                                                                                                       2          2                                                                                                                                                                                                                                                                   (4 + x)*(5 + x)*(7 + 2*x)                                                                                              |   3*(2 + x) *(3 + x) *(1 + x)*(x*((3 + x)*(7 + 5*x) + 4*(1 + x)*(2 + x)) + (1 + x)*(2 + x)*(3 + x))*|((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))*|----- + ----- + -------| + --------------------------------------------- + --------------------------------------------- + ---------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||    
        |    /       3 /       2            2                    \            2        3            2         /       2            2                    \            2                          \                     |    /       2 /       2            2                    \            2        2                                      \            2        2                    2                                                          \                                            \4 + x   5 + x   7 + 2*x/                       4 + x                                           5 + x                                          7 + 2*x                                                                                                       (4 + x)*(5 + x)*(7 + 2*x)                                                                                 /   2*(1 + x)*(2 + x)*(3 + x)*(x*((3 + x)*(7 + 5*x) + 4*(1 + x)*(2 + x)) + (1 + x)*(2 + x)*(3 + x))*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))|                     /       2 /       2            2                    \            2        2                                      \            2        3        3            2        2         /                                                                       x*(1 + x)*(2 + x)*(3 + x)*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))\   6*(2 + x)*(3 + x)*((7 + 2*x)*(22 + 5*x) + 10*(4 + x)*(5 + x))*\x*\(3 + x) *\(2 + x)  + 3*(1 + x)  + 6*(1 + x)*(2 + x)/ + 6*(1 + x) *(2 + x)  + 4*(1 + x)*(2 + x)*(3 + x)*(7 + 5*x)/ + 4*(1 + x) *(2 + x) *(3 + x) + (3 + x) *(1 + x)*(2 + x)*(7 + 5*x)/                                \                                              \(4 + x)    (5 + x)    (7 + 2*x)                                                           /                      (4 + x)                                          (5 + x)                                          (7 + 2*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          (4 + x)*(5 + x)*(7 + 2*x)                                                                                                                                                                     (4 + x)*(5 + x) *(7 + 2*x)                                                                                                                                                                    (4 + x) *(5 + x)*(7 + 2*x)                                                                                                                                                                                                                                                      (4 + x)*(5 + x) *(7 + 2*x)                                                                                                                                                                                                                                                                                                                                                                                           /                                                                                                     \                                            \4 + x   5 + x   7 + 2*x/                       4 + x                                           5 + x                                          7 + 2*x                                                                                                       (4 + x)*(5 + x)*(7 + 2*x)                                                                                 /|  -x
(3 + x)*|6*x*\(3 + x) *\(1 + x)  + 3*(2 + x)  + 6*(1 + x)*(2 + x)/ + 4*(1 + x) *(2 + x)  + 4*(3 + x) *(2 + x)*\(2 + x)  + 3*(1 + x)  + 6*(1 + x)*(2 + x)/ + 6*(2 + x) *(1 + x)*(3 + x)*(7 + 5*x)/ - 3*(2 + x)*(3 + x)*|2*x*\(3 + x) *\(2 + x)  + 3*(1 + x)  + 6*(1 + x)*(2 + x)/ + 6*(1 + x) *(2 + x)  + 4*(1 + x)*(2 + x)*(3 + x)*(7 + 5*x)/ + 8*(1 + x) *(2 + x) *(3 + x) + 2*(3 + x) *(1 + x)*(2 + x)*(7 + 5*x) + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------| + 6*(2 + x)*(3 + x)*\(3 + x) *\(2 + x)  + 3*(1 + x)  + 6*(1 + x)*(2 + x)/ + 6*(1 + x) *(2 + x)  + 4*(1 + x)*(2 + x)*(3 + x)*(7 + 5*x)/ - x*(1 + x) *(2 + x) *(3 + x)  - 3*(2 + x) *(3 + x) *(1 + x)*|-x*((3 + x)*(7 + 5*x) + 4*(1 + x)*(2 + x)) - (1 + x)*(2 + x)*(3 + x) + ---------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*e  
        \                                                                                                                                                                                                             \                                                                                                                                                                                                                                                                                                                                                                                                          (4 + x)*(5 + x)*(7 + 2*x)                                                                                                                                                                                                                                                                         (4 + x)*(5 + x)*(7 + 2*x)                                                         /                                                                                                                                                                                                     \                                                                                             (4 + x)*(5 + x)*(7 + 2*x)                      /                                                                                                                  (4 + x)*(5 + x)*(7 + 2*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        (4 + x)*(5 + x)*(7 + 2*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        (4 + x)*(5 + x)*(7 + 2*x)                                                                                                                                                                                                                                               /    
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              2        3          5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       (4 + x) *(5 + x) *(7 + 2*x)
(x+3)(−x(x+1)2(x+2)3(x+3)3−x(x+1)2(x+2)3(x+3)3(2(10(x+4)(x+5)+(2x+7)(5x+22))(60(2x+7)2+30(x+5)(2x+7)+6(x+5)2+20(x+4)(2x+7)+6(x+4)(x+5)+3(x+4)2)+10(10(x+4)(x+5)+(2x+7)(5x+22))(102x+7+3x+5+2x+4)2x+7+220(10(x+4)(x+5)+(2x+7)(5x+22))(2x+7)2+3(10(x+4)(x+5)+(2x+7)(5x+22))(102x+7+3x+5+2x+4)x+5+120(10(x+4)(x+5)+(2x+7)(5x+22))(x+5)(2x+7)+21(10(x+4)(x+5)+(2x+7)(5x+22))(x+5)2+2(10(x+4)(x+5)+(2x+7)(5x+22))(102x+7+3x+5+2x+4)x+4+80(10(x+4)(x+5)+(2x+7)(5x+22))(x+4)(2x+7)+24(10(x+4)(x+5)+(2x+7)(5x+22))(x+4)(x+5)−2(102x+7+3x+5+2x+4)(40(x+4)2(x+5)2+15(x+4)2(x+5)(2x+7)+10(x+4)(x+5)2(2x+7)+5(x+4)(x+5)(2x+7)(5x+22)+(2x+7)2(3(x+4)2+6(x+4)(x+5)+(x+5)2))(x+4)(x+5)(2x+7)−60(40(x+4)2(x+5)2+15(x+4)2(x+5)(2x+7)+10(x+4)(x+5)2(2x+7)+5(x+4)(x+5)(2x+7)(5x+22)+(2x+7)2(3(x+4)2+6(x+4)(x+5)+(x+5)2))(x+4)(x+5)(2x+7)2−18(40(x+4)2(x+5)2+15(x+4)2(x+5)(2x+7)+10(x+4)(x+5)2(2x+7)+5(x+4)(x+5)(2x+7)(5x+22)+(2x+7)2(3(x+4)2+6(x+4)(x+5)+(x+5)2))(x+4)(x+5)2(2x+7)+2(240(x+4)2(x+5)3+240(x+4)2(x+5)2(2x+7)+30(x+4)2(x+5)(2x+7)2+160(x+4)(x+5)3(2x+7)+60(x+4)(x+5)2(2x+7)2+40(x+4)(x+5)2(2x+7)(5x+22)+10(x+5)3(2x+7)2+20(x+5)(2x+7)2(3(x+4)2+6(x+4)(x+5)+(x+5)2)+3(2x+7)3((x+4)2+6(x+4)(x+5)+3(x+5)2))(x+4)(x+5)2(2x+7)2+10(10(x+4)(x+5)+(2x+7)(5x+22))(x+4)2−12(40(x+4)2(x+5)2+15(x+4)2(x+5)(2x+7)+10(x+4)(x+5)2(2x+7)+5(x+4)(x+5)(2x+7)(5x+22)+(2x+7)2(3(x+4)2+6(x+4)(x+5)+(x+5)2))(x+4)2(x+5)(2x+7))(x+4)(x+5)(2x+7)+6x(4(x+1)2(x+2)3+6(x+1)(x+2)2(x+3)(5x+7)+4(x+2)(x+3)2(3(x+1)2+6(x+1)(x+2)+(x+2)2)+(x+3)3((x+1)2+6(x+1)(x+2)+3(x+2)2))−3(x+1)(x+2)2(x+3)2(x(x+1)(x+2)(x+3)(10(x+4)(x+5)+(2x+7)(5x+22))(x+4)(x+5)(2x+7)−x(4(x+1)(x+2)+(x+3)(5x+7))−(x+1)(x+2)(x+3))+3(x+1)(x+2)2(x+3)2(x(4(x+1)(x+2)+(x+3)(5x+7))+(x+1)(x+2)(x+3))((10(x+4)(x+5)+(2x+7)(5x+22))(102x+7+3x+5+2x+4)+10(10(x+4)(x+5)+(2x+7)(5x+22))2x+7+3(10(x+4)(x+5)+(2x+7)(5x+22))x+5+2(10(x+4)(x+5)+(2x+7)(5x+22))x+4−2(40(x+4)2(x+5)2+15(x+4)2(x+5)(2x+7)+10(x+4)(x+5)2(2x+7)+5(x+4)(x+5)(2x+7)(5x+22)+(2x+7)2(3(x+4)2+6(x+4)(x+5)+(x+5)2))(x+4)(x+5)(2x+7))(x+4)(x+5)(2x+7)+6(x+2)(x+3)(6(x+1)2(x+2)2+4(x+1)(x+2)(x+3)(5x+7)+(x+3)2(3(x+1)2+6(x+1)(x+2)+(x+2)2))−3(x+2)(x+3)(x(x+1)2(x+2)2(x+3)2((10(x+4)(x+5)+(2x+7)(5x+22))(102x+7+3x+5+2x+4)+10(10(x+4)(x+5)+(2x+7)(5x+22))2x+7+3(10(x+4)(x+5)+(2x+7)(5x+22))x+5+2(10(x+4)(x+5)+(2x+7)(5x+22))x+4−2(40(x+4)2(x+5)2+15(x+4)2(x+5)(2x+7)+10(x+4)(x+5)2(2x+7)+5(x+4)(x+5)(2x+7)(5x+22)+(2x+7)2(3(x+4)2+6(x+4)(x+5)+(x+5)2))(x+4)(x+5)(2x+7))(x+4)(x+5)(2x+7)+2x(6(x+1)2(x+2)2+4(x+1)(x+2)(x+3)(5x+7)+(x+3)2(3(x+1)2+6(x+1)(x+2)+(x+2)2))+8(x+1)2(x+2)2(x+3)+2(x+1)(x+2)(x+3)2(5x+7)−2(x+1)(x+2)(x+3)(x(4(x+1)(x+2)+(x+3)(5x+7))+(x+1)(x+2)(x+3))(10(x+4)(x+5)+(2x+7)(5x+22))(x+4)(x+5)(2x+7))−6(x+2)(x+3)(10(x+4)(x+5)+(2x+7)(5x+22))(x(6(x+1)2(x+2)2+4(x+1)(x+2)(x+3)(5x+7)+(x+3)2(3(x+1)2+6(x+1)(x+2)+(x+2)2))+4(x+1)2(x+2)2(x+3)+(x+1)(x+2)(x+3)2(5x+7))(x+4)(x+5)(2x+7))e−x(x+4)2(x+5)3(2x+7)5\frac{\left(x + 3\right) \left(- x \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{3} - \frac{x \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{3} \left(2 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right) \left(\frac{60}{\left(2 x + 7\right)^{2}} + \frac{30}{\left(x + 5\right) \left(2 x + 7\right)} + \frac{6}{\left(x + 5\right)^{2}} + \frac{20}{\left(x + 4\right) \left(2 x + 7\right)} + \frac{6}{\left(x + 4\right) \left(x + 5\right)} + \frac{3}{\left(x + 4\right)^{2}}\right) + \frac{10 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right) \left(\frac{10}{2 x + 7} + \frac{3}{x + 5} + \frac{2}{x + 4}\right)}{2 x + 7} + \frac{220 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{\left(2 x + 7\right)^{2}} + \frac{3 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right) \left(\frac{10}{2 x + 7} + \frac{3}{x + 5} + \frac{2}{x + 4}\right)}{x + 5} + \frac{120 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{\left(x + 5\right) \left(2 x + 7\right)} + \frac{21 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{\left(x + 5\right)^{2}} + \frac{2 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right) \left(\frac{10}{2 x + 7} + \frac{3}{x + 5} + \frac{2}{x + 4}\right)}{x + 4} + \frac{80 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{\left(x + 4\right) \left(2 x + 7\right)} + \frac{24 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{\left(x + 4\right) \left(x + 5\right)} - \frac{2 \left(\frac{10}{2 x + 7} + \frac{3}{x + 5} + \frac{2}{x + 4}\right) \left(40 \left(x + 4\right)^{2} \left(x + 5\right)^{2} + 15 \left(x + 4\right)^{2} \left(x + 5\right) \left(2 x + 7\right) + 10 \left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right) + 5 \left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right) \left(5 x + 22\right) + \left(2 x + 7\right)^{2} \left(3 \left(x + 4\right)^{2} + 6 \left(x + 4\right) \left(x + 5\right) + \left(x + 5\right)^{2}\right)\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)} - \frac{60 \left(40 \left(x + 4\right)^{2} \left(x + 5\right)^{2} + 15 \left(x + 4\right)^{2} \left(x + 5\right) \left(2 x + 7\right) + 10 \left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right) + 5 \left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right) \left(5 x + 22\right) + \left(2 x + 7\right)^{2} \left(3 \left(x + 4\right)^{2} + 6 \left(x + 4\right) \left(x + 5\right) + \left(x + 5\right)^{2}\right)\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)^{2}} - \frac{18 \left(40 \left(x + 4\right)^{2} \left(x + 5\right)^{2} + 15 \left(x + 4\right)^{2} \left(x + 5\right) \left(2 x + 7\right) + 10 \left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right) + 5 \left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right) \left(5 x + 22\right) + \left(2 x + 7\right)^{2} \left(3 \left(x + 4\right)^{2} + 6 \left(x + 4\right) \left(x + 5\right) + \left(x + 5\right)^{2}\right)\right)}{\left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right)} + \frac{2 \left(240 \left(x + 4\right)^{2} \left(x + 5\right)^{3} + 240 \left(x + 4\right)^{2} \left(x + 5\right)^{2} \left(2 x + 7\right) + 30 \left(x + 4\right)^{2} \left(x + 5\right) \left(2 x + 7\right)^{2} + 160 \left(x + 4\right) \left(x + 5\right)^{3} \left(2 x + 7\right) + 60 \left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right)^{2} + 40 \left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right) \left(5 x + 22\right) + 10 \left(x + 5\right)^{3} \left(2 x + 7\right)^{2} + 20 \left(x + 5\right) \left(2 x + 7\right)^{2} \left(3 \left(x + 4\right)^{2} + 6 \left(x + 4\right) \left(x + 5\right) + \left(x + 5\right)^{2}\right) + 3 \left(2 x + 7\right)^{3} \left(\left(x + 4\right)^{2} + 6 \left(x + 4\right) \left(x + 5\right) + 3 \left(x + 5\right)^{2}\right)\right)}{\left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right)^{2}} + \frac{10 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{\left(x + 4\right)^{2}} - \frac{12 \left(40 \left(x + 4\right)^{2} \left(x + 5\right)^{2} + 15 \left(x + 4\right)^{2} \left(x + 5\right) \left(2 x + 7\right) + 10 \left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right) + 5 \left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right) \left(5 x + 22\right) + \left(2 x + 7\right)^{2} \left(3 \left(x + 4\right)^{2} + 6 \left(x + 4\right) \left(x + 5\right) + \left(x + 5\right)^{2}\right)\right)}{\left(x + 4\right)^{2} \left(x + 5\right) \left(2 x + 7\right)}\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)} + 6 x \left(4 \left(x + 1\right)^{2} \left(x + 2\right)^{3} + 6 \left(x + 1\right) \left(x + 2\right)^{2} \left(x + 3\right) \left(5 x + 7\right) + 4 \left(x + 2\right) \left(x + 3\right)^{2} \left(3 \left(x + 1\right)^{2} + 6 \left(x + 1\right) \left(x + 2\right) + \left(x + 2\right)^{2}\right) + \left(x + 3\right)^{3} \left(\left(x + 1\right)^{2} + 6 \left(x + 1\right) \left(x + 2\right) + 3 \left(x + 2\right)^{2}\right)\right) - 3 \left(x + 1\right) \left(x + 2\right)^{2} \left(x + 3\right)^{2} \left(\frac{x \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)} - x \left(4 \left(x + 1\right) \left(x + 2\right) + \left(x + 3\right) \left(5 x + 7\right)\right) - \left(x + 1\right) \left(x + 2\right) \left(x + 3\right)\right) + \frac{3 \left(x + 1\right) \left(x + 2\right)^{2} \left(x + 3\right)^{2} \left(x \left(4 \left(x + 1\right) \left(x + 2\right) + \left(x + 3\right) \left(5 x + 7\right)\right) + \left(x + 1\right) \left(x + 2\right) \left(x + 3\right)\right) \left(\left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right) \left(\frac{10}{2 x + 7} + \frac{3}{x + 5} + \frac{2}{x + 4}\right) + \frac{10 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{2 x + 7} + \frac{3 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{x + 5} + \frac{2 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{x + 4} - \frac{2 \left(40 \left(x + 4\right)^{2} \left(x + 5\right)^{2} + 15 \left(x + 4\right)^{2} \left(x + 5\right) \left(2 x + 7\right) + 10 \left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right) + 5 \left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right) \left(5 x + 22\right) + \left(2 x + 7\right)^{2} \left(3 \left(x + 4\right)^{2} + 6 \left(x + 4\right) \left(x + 5\right) + \left(x + 5\right)^{2}\right)\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)}\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)} + 6 \left(x + 2\right) \left(x + 3\right) \left(6 \left(x + 1\right)^{2} \left(x + 2\right)^{2} + 4 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(5 x + 7\right) + \left(x + 3\right)^{2} \left(3 \left(x + 1\right)^{2} + 6 \left(x + 1\right) \left(x + 2\right) + \left(x + 2\right)^{2}\right)\right) - 3 \left(x + 2\right) \left(x + 3\right) \left(\frac{x \left(x + 1\right)^{2} \left(x + 2\right)^{2} \left(x + 3\right)^{2} \left(\left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right) \left(\frac{10}{2 x + 7} + \frac{3}{x + 5} + \frac{2}{x + 4}\right) + \frac{10 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{2 x + 7} + \frac{3 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{x + 5} + \frac{2 \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{x + 4} - \frac{2 \left(40 \left(x + 4\right)^{2} \left(x + 5\right)^{2} + 15 \left(x + 4\right)^{2} \left(x + 5\right) \left(2 x + 7\right) + 10 \left(x + 4\right) \left(x + 5\right)^{2} \left(2 x + 7\right) + 5 \left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right) \left(5 x + 22\right) + \left(2 x + 7\right)^{2} \left(3 \left(x + 4\right)^{2} + 6 \left(x + 4\right) \left(x + 5\right) + \left(x + 5\right)^{2}\right)\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)}\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)} + 2 x \left(6 \left(x + 1\right)^{2} \left(x + 2\right)^{2} + 4 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(5 x + 7\right) + \left(x + 3\right)^{2} \left(3 \left(x + 1\right)^{2} + 6 \left(x + 1\right) \left(x + 2\right) + \left(x + 2\right)^{2}\right)\right) + 8 \left(x + 1\right)^{2} \left(x + 2\right)^{2} \left(x + 3\right) + 2 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right)^{2} \left(5 x + 7\right) - \frac{2 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(x \left(4 \left(x + 1\right) \left(x + 2\right) + \left(x + 3\right) \left(5 x + 7\right)\right) + \left(x + 1\right) \left(x + 2\right) \left(x + 3\right)\right) \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)}\right) - \frac{6 \left(x + 2\right) \left(x + 3\right) \left(10 \left(x + 4\right) \left(x + 5\right) + \left(2 x + 7\right) \left(5 x + 22\right)\right) \left(x \left(6 \left(x + 1\right)^{2} \left(x + 2\right)^{2} + 4 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(5 x + 7\right) + \left(x + 3\right)^{2} \left(3 \left(x + 1\right)^{2} + 6 \left(x + 1\right) \left(x + 2\right) + \left(x + 2\right)^{2}\right)\right) + 4 \left(x + 1\right)^{2} \left(x + 2\right)^{2} \left(x + 3\right) + \left(x + 1\right) \left(x + 2\right) \left(x + 3\right)^{2} \left(5 x + 7\right)\right)}{\left(x + 4\right) \left(x + 5\right) \left(2 x + 7\right)}\right) e^{- x}}{\left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5}}
Simplificar
Gráfico
Derivada de x*((x+1)^2*(x+2)^3*(x+3)^4)/((x+4)^2*(x+5)^3*(2x+7)^5)exp(-x)
    © Sr Examen – Калькулятор