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Derivada de:
Derivada de (π*n)/30
Derivada de √π*e^(x√2)/√2
Derivada de (π/3)-x
Derivada de (а+в+с)^2
Expresiones idénticas
x*((x+ uno)^ dos *(x+ dos)^ tres *(x+ tres)^ cuatro)/((x+ cuatro)^ dos *(x+ cinco)^ tres *(2x+ siete)^ cinco)exp(-x)
x multiplicar por ((x más 1) al cuadrado multiplicar por (x más 2) al cubo multiplicar por (x más 3) en el grado 4) dividir por ((x más 4) al cuadrado multiplicar por (x más 5) al cubo multiplicar por (2x más 7) en el grado 5) exponente de ( menos x)
x multiplicar por ((x más uno) en el grado dos multiplicar por (x más dos) en el grado tres multiplicar por (x más tres) en el grado cuatro) dividir por ((x más cuatro) en el grado dos multiplicar por (x más cinco) en el grado tres multiplicar por (2x más siete) en el grado cinco) exponente de ( menos x)
x*((x+1)2*(x+2)3*(x+3)4)/((x+4)2*(x+5)3*(2x+7)5)exp(-x)
x*x+12*x+23*x+34/x+42*x+53*2x+75exp-x
x*((x+1)²*(x+2)³*(x+3)⁴)/((x+4)²*(x+5)³*(2x+7)⁵)exp(-x)
x*((x+1) en el grado 2*(x+2) en el grado 3*(x+3) en el grado 4)/((x+4) en el grado 2*(x+5) en el grado 3*(2x+7) en el grado 5)exp(-x)
x((x+1)^2(x+2)^3(x+3)^4)/((x+4)^2(x+5)^3(2x+7)^5)exp(-x)
x((x+1)2(x+2)3(x+3)4)/((x+4)2(x+5)3(2x+7)5)exp(-x)
xx+12x+23x+34/x+42x+532x+75exp-x
xx+1^2x+2^3x+3^4/x+4^2x+5^32x+7^5exp-x
x*((x+1)^2*(x+2)^3*(x+3)^4) dividir por ((x+4)^2*(x+5)^3*(2x+7)^5)exp(-x)
Expresiones semejantes
x*((x+1)^2*(x+2)^3*(x+3)^4)/((x+4)^2*(x-5)^3*(2x+7)^5)exp(-x)
x*((x+1)^2*(x+2)^3*(x+3)^4)/((x+4)^2*(x+5)^3*(2x+7)^5)exp(x)
x*((x+1)^2*(x-2)^3*(x+3)^4)/((x+4)^2*(x+5)^3*(2x+7)^5)exp(-x)
x*((x+1)^2*(x+2)^3*(x+3)^4)/((x+4)^2*(x+5)^3*(2x-7)^5)exp(-x)
x*((x-1)^2*(x+2)^3*(x+3)^4)/((x+4)^2*(x+5)^3*(2x+7)^5)exp(-x)
x*((x+1)^2*(x+2)^3*(x-3)^4)/((x+4)^2*(x+5)^3*(2x+7)^5)exp(-x)
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)

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)

$$\frac{x \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{4}}{\left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5}} e^{- x}$$

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

Solución detallada

Se aplica la regla de la derivada parcial:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

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

Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
1. Se aplica la regla de la derivada de una multiplicación:
  
  $\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} = \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{3}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{2}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{1}}{\left(x \right)} + \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}$
  
  $\operatorname{f_{0}}{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}$ :
  1. Según el principio, aplicamos: $x$ tenemos $1$
  $\operatorname{f_{1}}{\left(x \right)} = \left(x + 1\right)^{2}$ ; calculamos $\frac{d}{d x} \operatorname{f_{1}}{\left(x \right)}$ :
  1. Sustituimos $u = x + 1$ .
  2. Según el principio, aplicamos: $u^{2}$ tenemos $2 u$
  3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(x + 1\right)$ :
    1. diferenciamos $x + 1$ miembro por miembro:
      1. La derivada de una constante $1$ es igual a cero.
      2. Según el principio, aplicamos: $x$ tenemos $1$
      Como resultado de: $1$
    Como resultado de la secuencia de reglas:
    
    $2 x + 2$
  $\operatorname{f_{2}}{\left(x \right)} = \left(x + 2\right)^{3}$ ; calculamos $\frac{d}{d x} \operatorname{f_{2}}{\left(x \right)}$ :
  1. Sustituimos $u = x + 2$ .
  2. Según el principio, aplicamos: $u^{3}$ tenemos $3 u^{2}$
  3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(x + 2\right)$ :
    1. diferenciamos $x + 2$ miembro por miembro:
      1. La derivada de una constante $2$ es igual a cero.
      2. Según el principio, aplicamos: $x$ tenemos $1$
      Como resultado de: $1$
    Como resultado de la secuencia de reglas:
    
    $3 \left(x + 2\right)^{2}$
  $\operatorname{f_{3}}{\left(x \right)} = \left(x + 3\right)^{4}$ ; calculamos $\frac{d}{d x} \operatorname{f_{3}}{\left(x \right)}$ :
  1. Sustituimos $u = x + 3$ .
  2. Según el principio, aplicamos: $u^{4}$ tenemos $4 u^{3}$
  3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(x + 3\right)$ :
    1. diferenciamos $x + 3$ miembro por miembro:
      1. La derivada de una constante $3$ es igual a cero.
      2. Según el principio, aplicamos: $x$ tenemos $1$
      Como resultado de: $1$
    Como resultado de la secuencia de reglas:
    
    $4 \left(x + 3\right)^{3}$
  Como resultado de: $4 x \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{3} + 3 x \left(x + 1\right)^{2} \left(x + 2\right)^{2} \left(x + 3\right)^{4} + x \left(x + 2\right)^{3} \left(x + 3\right)^{4} \left(2 x + 2\right) + \left(x + 1\right)^{2} \left(x + 2\right)^{3} \left(x + 3\right)^{4}$
Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
1. Se aplica la regla de la derivada de una multiplicación:
  
  $\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} = \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{3}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{2}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{1}}{\left(x \right)} + \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}$
  
  $\operatorname{f_{0}}{\left(x \right)} = \left(x + 4\right)^{2}$ ; calculamos $\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}$ :
  1. Sustituimos $u = x + 4$ .
  2. Según el principio, aplicamos: $u^{2}$ tenemos $2 u$
  3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(x + 4\right)$ :
    1. diferenciamos $x + 4$ miembro por miembro:
      1. La derivada de una constante $4$ es igual a cero.
      2. Según el principio, aplicamos: $x$ tenemos $1$
      Como resultado de: $1$
    Como resultado de la secuencia de reglas:
    
    $2 x + 8$
  $\operatorname{f_{1}}{\left(x \right)} = \left(x + 5\right)^{3}$ ; calculamos $\frac{d}{d x} \operatorname{f_{1}}{\left(x \right)}$ :
  1. Sustituimos $u = x + 5$ .
  2. Según el principio, aplicamos: $u^{3}$ tenemos $3 u^{2}$
  3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(x + 5\right)$ :
    1. diferenciamos $x + 5$ miembro por miembro:
      1. La derivada de una constante $5$ es igual a cero.
      2. Según el principio, aplicamos: $x$ tenemos $1$
      Como resultado de: $1$
    Como resultado de la secuencia de reglas:
    
    $3 \left(x + 5\right)^{2}$
  $\operatorname{f_{2}}{\left(x \right)} = \left(2 x + 7\right)^{5}$ ; calculamos $\frac{d}{d x} \operatorname{f_{2}}{\left(x \right)}$ :
  1. Sustituimos $u = 2 x + 7$ .
  2. Según el principio, aplicamos: $u^{5}$ tenemos $5 u^{4}$
  3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(2 x + 7\right)$ :
    1. diferenciamos $2 x + 7$ miembro por miembro:
      1. La derivada de una constante $7$ 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.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Entonces, como resultado: $2$
      Como resultado de: $2$
    Como resultado de la secuencia de reglas:
    
    $10 \left(2 x + 7\right)^{4}$
  $\operatorname{f_{3}}{\left(x \right)} = e^{x}$ ; calculamos $\frac{d}{d x} \operatorname{f_{3}}{\left(x \right)}$ :
  1. Derivado $e^{x}$ es.
  Como resultado de: $\left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{5} e^{x} + 10 \left(x + 4\right)^{2} \left(x + 5\right)^{3} \left(2 x + 7\right)^{4} e^{x} + 3 \left(x + 4\right)^{2} \left(x + 5\right)^{2} \left(2 x + 7\right)^{5} e^{x} + \left(x + 5\right)^{3} \left(2 x + 7\right)^{5} \left(2 x + 8\right) e^{x}$
Ahora aplicamos la regla de la derivada de una divesión:

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

$\frac{\left(- 2 x^{13} - 65 x^{12} - 912 x^{11} - 7235 x^{10} - 35316 x^{9} - 105411 x^{8} - 160246 x^{7} + 61331 x^{6} + 863130 x^{5} + 1969460 x^{4} + 2400762 x^{3} + 1682208 x^{2} + 623592 x + 90720\right) e^{- x}}{64 x^{13} + 3392 x^{12} + 82800 x^{11} + 1232608 x^{10} + 12485276 x^{9} + 90870804 x^{8} + 488932137 x^{7} + 1969144200 x^{6} + 5936402178 x^{5} + 13231328096 x^{4} + 21193220545 x^{3} + 23102181900 x^{2} + 15361598000 x + 4705960000}$

Respuesta:

$\frac{\left(- 2 x^{13} - 65 x^{12} - 912 x^{11} - 7235 x^{10} - 35316 x^{9} - 105411 x^{8} - 160246 x^{7} + 61331 x^{6} + 863130 x^{5} + 1969460 x^{4} + 2400762 x^{3} + 1682208 x^{2} + 623592 x + 90720\right) e^{- x}}{64 x^{13} + 3392 x^{12} + 82800 x^{11} + 1232608 x^{10} + 12485276 x^{9} + 90870804 x^{8} + 488932137 x^{7} + 1969144200 x^{6} + 5936402178 x^{5} + 13231328096 x^{4} + 21193220545 x^{3} + 23102181900 x^{2} + 15361598000 x + 4705960000}$

Gráfica

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)

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

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)

$$\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)

$$\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}}$$

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Gráfico

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

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Expresiones semejantes

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

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

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

Gráfico:

Definida a trozos:

Solución

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