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y=((cos(x))^7*(3*x+2))/((x^2+6)^(3/4)*(5*x-7*x*x)^11)

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  • Derivada de:
  • Derivada de 2^-x^3 Derivada de 2^-x^3
  • Derivada de 2*x^-1 Derivada de 2*x^-1
  • Derivada de 2^(x+1)+3^(x-1) Derivada de 2^(x+1)+3^(x-1)
  • Derivada de (2x)^1/3 Derivada de (2x)^1/3

  • Expresiones idénticas

  • y=((cos(x))^ siete *(tres *x+ dos))/((x^ dos + seis)^(tres / cuatro)*(cinco *x- siete *x*x)^ once)
  • y es igual a (( coseno de (x)) en el grado 7 multiplicar por (3 multiplicar por x más 2)) dividir por ((x al cuadrado más 6) en el grado (3 dividir por 4) multiplicar por (5 multiplicar por x menos 7 multiplicar por x multiplicar por x) en el grado 11)
  • y es igual a (( coseno de (x)) en el grado siete multiplicar por (tres multiplicar por x más dos)) dividir por ((x en el grado dos más seis) en el grado (tres dividir por cuatro) multiplicar por (cinco multiplicar por x menos siete multiplicar por x multiplicar por x) en el grado once)
  • y=((cos(x))7*(3*x+2))/((x2+6)(3/4)*(5*x-7*x*x)11)
  • y=cosx7*3*x+2/x2+63/4*5*x-7*x*x11
  • y=((cos(x))⁷*(3*x+2))/((x²+6)^(3/4)*(5*x-7*x*x)^11)
  • y=((cos(x)) en el grado 7*(3*x+2))/((x en el grado 2+6) en el grado (3/4)*(5*x-7*x*x) en el grado 11)
  • y=((cos(x))^7(3x+2))/((x^2+6)^(3/4)(5x-7xx)^11)
  • y=((cos(x))7(3x+2))/((x2+6)(3/4)(5x-7xx)11)
  • y=cosx73x+2/x2+63/45x-7xx11
  • y=cosx^73x+2/x^2+6^3/45x-7xx^11
  • y=((cos(x))^7*(3*x+2)) dividir por ((x^2+6)^(3 dividir por 4)*(5*x-7*x*x)^11)

  • Expresiones semejantes

  • y=((cos(x))^7*(3*x+2))/((x^2-6)^(3/4)*(5*x-7*x*x)^11)
  • y=((cos(x))^7*(3*x-2))/((x^2+6)^(3/4)*(5*x-7*x*x)^11)
  • y=((cos(x))^7*(3*x+2))/((x^2+6)^(3/4)*(5*x+7*x*x)^11)
  • y=((cosx)^7*(3*x+2))/((x^2+6)^(3/4)*(5*x-7*x*x)^11)
Derivada de la función/ y=((cos(x))^7*(3*x+2))/((x^2+6)^(3/4)*(5*x-7*x*x)^11)

Derivada de y=((cos(x))^7*(3*x+2))/((x^2+6)^(3/4)*(5*x-7*x*x)^11)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
        7                  
     cos (x)*(3*x + 2)     
---------------------------
        3/4                
/ 2    \                 11
\x  + 6/   *(5*x - 7*x*x)
(3x+2)cos⁡7(x)(x2+6)34(−x7x+5x)11\frac{\left(3 x + 2\right) \cos^{7}{\left(x \right)}}{\left(x^{2} + 6\right)^{\frac{3}{4}} \left(- x 7 x + 5 x\right)^{11}} 
(cos(x)^7*(3*x + 2))/(((x^2 + 6)^(3/4)*(5*x - 7*x*x)^11))
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)=(3x+2)cos⁡7(x)f{\left(x \right)} = \left(3 x + 2\right) \cos^{7}{\left(x \right)} y g(x)=(−7x2+5x)11(x2+6)34g{\left(x \right)} = \left(- 7 x^{2} + 5 x\right)^{11} \left(x^{2} + 6\right)^{\frac{3}{4}}.

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

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

      ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

      f(x)=cos⁡7(x)f{\left(x \right)} = \cos^{7}{\left(x \right)}; calculamos ddxf(x)\frac{d}{d x} f{\left(x \right)}:

      1. Sustituimos u=cos⁡(x)u = \cos{\left(x \right)}.

      2. Según el principio, aplicamos: u7u^{7} tenemos 7u67 u^{6}

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

        1. La derivada del coseno es igual a menos el seno:

          ddxcos⁡(x)=−sin⁡(x)\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}

        Como resultado de la secuencia de reglas:

        −7sin⁡(x)cos⁡6(x)- 7 \sin{\left(x \right)} \cos^{6}{\left(x \right)}

      g(x)=3x+2g{\left(x \right)} = 3 x + 2; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

      1. diferenciamos 3x+23 x + 2 miembro por miembro:

        1. La derivada de una constante 22 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: 33

        Como resultado de: 33

      Como resultado de: −7(3x+2)sin⁡(x)cos⁡6(x)+3cos⁡7(x)- 7 \left(3 x + 2\right) \sin{\left(x \right)} \cos^{6}{\left(x \right)} + 3 \cos^{7}{\left(x \right)}

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

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

      ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

      f(x)=(x2+6)34f{\left(x \right)} = \left(x^{2} + 6\right)^{\frac{3}{4}}; calculamos ddxf(x)\frac{d}{d x} f{\left(x \right)}:

      1. Sustituimos u=x2+6u = x^{2} + 6.

      2. Según el principio, aplicamos: u34u^{\frac{3}{4}} tenemos 34u4\frac{3}{4 \sqrt[4]{u}}

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(x2+6)\frac{d}{d x} \left(x^{2} + 6\right):

        1. diferenciamos x2+6x^{2} + 6 miembro por miembro:

          1. La derivada de una constante 66 es igual a cero.

          2. Según el principio, aplicamos: x2x^{2} tenemos 2x2 x

          Como resultado de: 2x2 x

        Como resultado de la secuencia de reglas:

        3x2x2+64\frac{3 x}{2 \sqrt[4]{x^{2} + 6}}

      g(x)=(−7x2+5x)11g{\left(x \right)} = \left(- 7 x^{2} + 5 x\right)^{11}; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

      1. Sustituimos u=−7x2+5xu = - 7 x^{2} + 5 x.

      2. Según el principio, aplicamos: u11u^{11} tenemos 11u1011 u^{10}

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(−7x2+5x)\frac{d}{d x} \left(- 7 x^{2} + 5 x\right):

        1. diferenciamos −7x2+5x- 7 x^{2} + 5 x miembro por miembro:

          1. 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: x2x^{2} tenemos 2x2 x

            Entonces, como resultado: −14x- 14 x

          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: 55

          Como resultado de: 5−14x5 - 14 x

        Como resultado de la secuencia de reglas:

        11(5−14x)(−7x2+5x)1011 \left(5 - 14 x\right) \left(- 7 x^{2} + 5 x\right)^{10}

      Como resultado de: 3x(−7x2+5x)112x2+64+11(5−14x)(−7x2+5x)10(x2+6)34\frac{3 x \left(- 7 x^{2} + 5 x\right)^{11}}{2 \sqrt[4]{x^{2} + 6}} + 11 \left(5 - 14 x\right) \left(- 7 x^{2} + 5 x\right)^{10} \left(x^{2} + 6\right)^{\frac{3}{4}}

    Ahora aplicamos la regla de la derivada de una divesión:

    −(3x+2)(3x(−7x2+5x)112x2+64+11(5−14x)(−7x2+5x)10(x2+6)34)cos⁡7(x)+(−7x2+5x)11(x2+6)34(−7(3x+2)sin⁡(x)cos⁡6(x)+3cos⁡7(x))(−7x2+5x)22(x2+6)32\frac{- \left(3 x + 2\right) \left(\frac{3 x \left(- 7 x^{2} + 5 x\right)^{11}}{2 \sqrt[4]{x^{2} + 6}} + 11 \left(5 - 14 x\right) \left(- 7 x^{2} + 5 x\right)^{10} \left(x^{2} + 6\right)^{\frac{3}{4}}\right) \cos^{7}{\left(x \right)} + \left(- 7 x^{2} + 5 x\right)^{11} \left(x^{2} + 6\right)^{\frac{3}{4}} \left(- 7 \left(3 x + 2\right) \sin{\left(x \right)} \cos^{6}{\left(x \right)} + 3 \cos^{7}{\left(x \right)}\right)}{\left(- 7 x^{2} + 5 x\right)^{22} \left(x^{2} + 6\right)^{\frac{3}{2}}}

  2. Simplificamos:

    (x(7x−5)(x2+6)((21x+14)sin⁡(x)−3cos⁡(x))−(3x+2)(x2(15−21x)−22(14x−5)(x2+6))cos⁡(x)2)cos⁡6(x)x12(7x−5)12(x2+6)74\frac{\left(x \left(7 x - 5\right) \left(x^{2} + 6\right) \left(\left(21 x + 14\right) \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right) - \frac{\left(3 x + 2\right) \left(x^{2} \left(15 - 21 x\right) - 22 \left(14 x - 5\right) \left(x^{2} + 6\right)\right) \cos{\left(x \right)}}{2}\right) \cos^{6}{\left(x \right)}}{x^{12} \left(7 x - 5\right)^{12} \left(x^{2} + 6\right)^{\frac{7}{4}}}

Respuesta:

(x(7x−5)(x2+6)((21x+14)sin⁡(x)−3cos⁡(x))−(3x+2)(x2(15−21x)−22(14x−5)(x2+6))cos⁡(x)2)cos⁡6(x)x12(7x−5)12(x2+6)74\frac{\left(x \left(7 x - 5\right) \left(x^{2} + 6\right) \left(\left(21 x + 14\right) \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right) - \frac{\left(3 x + 2\right) \left(x^{2} \left(15 - 21 x\right) - 22 \left(14 x - 5\right) \left(x^{2} + 6\right)\right) \cos{\left(x \right)}}{2}\right) \cos^{6}{\left(x \right)}}{x^{12} \left(7 x - 5\right)^{12} \left(x^{2} + 6\right)^{\frac{7}{4}}}

Gráfica
02468-8-6-4-2-1010-20000000000000000002000000000000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                                                                         /          3/4                                                 11\
                                                                          7              |  / 2    \                 10                3*x*(5*x - 7*x*x)  |
                                                                       cos (x)*(3*x + 2)*|- \x  + 6/   *(5*x - 7*x*x)  *(55 - 154*x) - -------------------|
                                                                                         |                                                     ________   |
                                                                                         |                                                  4 /  2        |
             1              /     7           6                    \                     \                                                2*\/  x  + 6    /
---------------------------*\3*cos (x) - 7*cos (x)*(3*x + 2)*sin(x)/ + ------------------------------------------------------------------------------------
        3/4                                                                                                3/2                                             
/ 2    \                 11                                                                        / 2    \                 22                             
\x  + 6/   *(5*x - 7*x*x)                                                                          \x  + 6/   *(5*x - 7*x*x)
1(x2+6)34(−x7x+5x)11(−7(3x+2)sin⁡(x)cos⁡6(x)+3cos⁡7(x))+(3x+2)(−3x(−x7x+5x)112x2+64−(55−154x)(x2+6)34(−x7x+5x)10)cos⁡7(x)(x2+6)32(−x7x+5x)22\frac{1}{\left(x^{2} + 6\right)^{\frac{3}{4}} \left(- x 7 x + 5 x\right)^{11}} \left(- 7 \left(3 x + 2\right) \sin{\left(x \right)} \cos^{6}{\left(x \right)} + 3 \cos^{7}{\left(x \right)}\right) + \frac{\left(3 x + 2\right) \left(- \frac{3 x \left(- x 7 x + 5 x\right)^{11}}{2 \sqrt[4]{x^{2} + 6}} - \left(55 - 154 x\right) \left(x^{2} + 6\right)^{\frac{3}{4}} \left(- x 7 x + 5 x\right)^{10}\right) \cos^{7}{\left(x \right)}}{\left(x^{2} + 6\right)^{\frac{3}{2}} \left(- x 7 x + 5 x\right)^{22}}
Simplificar
Segunda derivada [src] 
         /                                                                            /                                                                             /           3/4                  2           \                            3/4      4           2      2           2                 3/4                   2                                         /           3/4                  2           \\                                                                                         \ 
         |                                                                            |                                                                             |   /     2\                  3*x *(-5 + 7*x)|                  2 /     2\      3*x *(-5 + 7*x)    6*x *(-5 + 7*x)          /     2\                 132*x *(-5 + 7*x)*(-5 + 14*x)                  |   /     2\                  3*x *(-5 + 7*x)||                                                                                         | 
         |                                                                            |                                                                           3*|22*\6 + x /   *(-5 + 14*x) + ---------------|   440*(-5 + 14*x) *\6 + x /    - ---------------- + ---------------- + 616*x*\6 + x /   *(-5 + 7*x) + -----------------------------   22*(-5 + 14*x)*|22*\6 + x /   *(-5 + 14*x) + ---------------||                                                                                         | 
         |                                                                            |                                                                             |                                  ________  |                                            5/4           ________                                                 ________                           |                                  ________  ||                                                                                         | 
         |                                                                            |                          /           3/4                  2           \     |                               4 /      2   |                                    /     2\           4 /      2                                               4 /      2                            |                               4 /      2   ||                                    /           3/4                  2           \       | 
         |                                                             2              |/  3      22*(-5 + 14*x)\ |   /     2\                  3*x *(-5 + 7*x)|     \                               \/  6 + x    /                                    \6 + x /           \/  6 + x                                                \/  6 + x                             \                               \/  6 + x    /|                                    |   /     2\                  3*x *(-5 + 7*x)|       | 
         |                                                          cos (x)*(2 + 3*x)*||------ + --------------|*|22*\6 + x /   *(-5 + 14*x) + ---------------| + ------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------|   (-3*cos(x) + 7*(2 + 3*x)*sin(x))*|22*\6 + x /   *(-5 + 14*x) + ---------------|*cos(x)| 
         |                                                                            ||     2    2            | |                                  ________  |                             2                                                                                   2                                                                                                 2                                   |                                    |                                  ________  |       | 
         |  /          /     2           2   \                  \                     |\6 + x    x *(-5 + 7*x) / |                               4 /      2   |                        6 + x                                                                                   x *(-5 + 7*x)                                                                                     x *(-5 + 7*x)                        |                                    |                               4 /      2   |       | 
    5    |7*\(2 + 3*x)*\- cos (x) + 6*sin (x)/ - 6*cos(x)*sin(x)/                     \                          \                               \/  6 + x    /                                                                                                                                                                                                                                                       /                                    \                               \/  6 + x    /       | 
-cos (x)*|------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------| 
         |                              3/4                                                                                                                                                                                                            3/2                                                                                                                                                                                                                    3/2                               | 
         |                      /     2\                                                                                                                                                                                                       /     2\                                                                                                                                                                                                               /     2\                                  | 
         \                      \6 + x /                                                                                                                                                                                          4*(-5 + 7*x)*\6 + x /                                                                                                                                                                                                  x*(-5 + 7*x)*\6 + x /                                  / 
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                  11           11                                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                                 x  *(-5 + 7*x)
−((3x+2)((3x2(7x−5)x2+64+22(14x−5)(x2+6)34)(3x2+6+22(14x−5)x2(7x−5))+3(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)x2+6+22(14x−5)(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)x2(7x−5)−−3x4(7x−5)2(x2+6)54+6x2(7x−5)2x2+64+132x2(7x−5)(14x−5)x2+64+616x(7x−5)(x2+6)34+440(14x−5)2(x2+6)34x2(7x−5))cos⁡2(x)4(7x−5)(x2+6)32+7((3x+2)(6sin⁡2(x)−cos⁡2(x))−6sin⁡(x)cos⁡(x))(x2+6)34+(7(3x+2)sin⁡(x)−3cos⁡(x))(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)cos⁡(x)x(7x−5)(x2+6)32)cos⁡5(x)x11(7x−5)11- \frac{\left(\frac{\left(3 x + 2\right) \left(\left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right) \left(\frac{3}{x^{2} + 6} + \frac{22 \left(14 x - 5\right)}{x^{2} \left(7 x - 5\right)}\right) + \frac{3 \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{2} + 6} + \frac{22 \left(14 x - 5\right) \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{2} \left(7 x - 5\right)} - \frac{- \frac{3 x^{4} \left(7 x - 5\right)^{2}}{\left(x^{2} + 6\right)^{\frac{5}{4}}} + \frac{6 x^{2} \left(7 x - 5\right)^{2}}{\sqrt[4]{x^{2} + 6}} + \frac{132 x^{2} \left(7 x - 5\right) \left(14 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 616 x \left(7 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}} + 440 \left(14 x - 5\right)^{2} \left(x^{2} + 6\right)^{\frac{3}{4}}}{x^{2} \left(7 x - 5\right)}\right) \cos^{2}{\left(x \right)}}{4 \left(7 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{2}}} + \frac{7 \left(\left(3 x + 2\right) \left(6 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 6 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{\left(x^{2} + 6\right)^{\frac{3}{4}}} + \frac{\left(7 \left(3 x + 2\right) \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right) \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right) \cos{\left(x \right)}}{x \left(7 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{2}}}\right) \cos^{5}{\left(x \right)}}{x^{11} \left(7 x - 5\right)^{11}}
Simplificar
Tercera derivada [src] 
        /                                                                                                          /                                                                                                                                          /           3/4                  2           \       /           3/4                  2           \     /           3/4                  2           \     /                          3/4      4           3      6           3         3           2       4           2                    2           2                     2            2                              3/4                       \                               /           3/4                  2           \                             /                         3/4      4           2      2           2                 3/4                   2                       \                  /                         3/4      4           2      2           2                 3/4                   2                       \     /                         3/4      4           2      2           2                 3/4                   2                       \                     /           3/4                  2           \                                            /           3/4                  2           \                   /           3/4                  2           \\                                              /                                                                             /           3/4                  2           \                            3/4      4           2      2           2                 3/4                   2                                         /           3/4                  2           \\                                                                                                                 \
        |                                                                                                          |                                                                                                                                          |   /     2\                  3*x *(-5 + 7*x)|       |   /     2\                  3*x *(-5 + 7*x)|     |   /     2\                  3*x *(-5 + 7*x)|     |                3 /     2\      6*x *(-5 + 7*x)    5*x *(-5 + 7*x)    1848*x *(-5 + 7*x)    66*x *(-5 + 7*x) *(-5 + 14*x)   132*x *(-5 + 7*x) *(-5 + 14*x)   1320*x *(-5 + 14*x) *(-5 + 7*x)           /     2\                          |     /  3      22*(-5 + 14*x)\ |   /     2\                  3*x *(-5 + 7*x)|   /  3      22*(-5 + 14*x)\ |               2 /     2\      3*x *(-5 + 7*x)    6*x *(-5 + 7*x)          /     2\                 132*x *(-5 + 7*x)*(-5 + 14*x)|                  |               2 /     2\      3*x *(-5 + 7*x)    6*x *(-5 + 7*x)          /     2\                 132*x *(-5 + 7*x)*(-5 + 14*x)|     |               2 /     2\      3*x *(-5 + 7*x)    6*x *(-5 + 7*x)          /     2\                 132*x *(-5 + 7*x)*(-5 + 14*x)|                   2 |   /     2\                  3*x *(-5 + 7*x)|                  /  3      22*(-5 + 14*x)\ |   /     2\                  3*x *(-5 + 7*x)|                   |   /     2\                  3*x *(-5 + 7*x)||                                              |                                                                             |   /     2\                  3*x *(-5 + 7*x)|                  2 /     2\      3*x *(-5 + 7*x)    6*x *(-5 + 7*x)          /     2\                 132*x *(-5 + 7*x)*(-5 + 14*x)                  |   /     2\                  3*x *(-5 + 7*x)||                                                                                                                 |
        |                                                                                                          |                                                                                                                                       30*|22*\6 + x /   *(-5 + 14*x) + ---------------|   616*|22*\6 + x /   *(-5 + 14*x) + ---------------|   6*|22*\6 + x /   *(-5 + 14*x) + ---------------|   3*|2640*(-5 + 14*x) *\6 + x /    - ---------------- + ---------------- + ------------------- - ----------------------------- + ------------------------------ + ------------------------------- + 12320*x*\6 + x /   *(-5 + 7*x)*(-5 + 14*x)|   3*|------ + --------------|*|22*\6 + x /   *(-5 + 14*x) + ---------------|   |------ + --------------|*|440*(-5 + 14*x) *\6 + x /    - ---------------- + ---------------- + 616*x*\6 + x /   *(-5 + 7*x) + -----------------------------|   66*(-5 + 14*x)*|440*(-5 + 14*x) *\6 + x /    - ---------------- + ---------------- + 616*x*\6 + x /   *(-5 + 7*x) + -----------------------------|   9*|440*(-5 + 14*x) *\6 + x /    - ---------------- + ---------------- + 616*x*\6 + x /   *(-5 + 7*x) + -----------------------------|   1012*(-5 + 14*x) *|22*\6 + x /   *(-5 + 14*x) + ---------------|   22*(-5 + 14*x)*|------ + --------------|*|22*\6 + x /   *(-5 + 14*x) + ---------------|   264*(-5 + 14*x)*|22*\6 + x /   *(-5 + 14*x) + ---------------||                                              |                                                                           3*|22*\6 + x /   *(-5 + 14*x) + ---------------|   440*(-5 + 14*x) *\6 + x /    - ---------------- + ---------------- + 616*x*\6 + x /   *(-5 + 7*x) + -----------------------------   22*(-5 + 14*x)*|22*\6 + x /   *(-5 + 14*x) + ---------------||                                                                                                                 |
        |                                                                                                          |                                                                                                                                          |                                  ________  |       |                                  ________  |     |                                  ________  |     |                                          5/4                9/4             ________                        5/4                        ________                          ________                                                       |     |     2    2            | |                                  ________  |   |     2    2            | |                                         5/4           ________                                                 ________         |                  |                                         5/4           ________                                                 ________         |     |                                         5/4           ________                                                 ________         |                     |                                  ________  |                  |     2    2            | |                                  ________  |                   |                                  ________  ||                                              |                                                                             |                                  ________  |                                            5/4           ________                                                 ________                           |                                  ________  ||                                                                                                                 |
        |                                                                                                          |/           3/4                  2           \ /                                                         2                         \      |                               4 /      2   |       |                               4 /      2   |     |                               4 /      2   |     |                                  /     2\           /     2\             4 /      2                 /     2\                        4 /      2                        4 /      2                                                        |     \6 + x    x *(-5 + 7*x) / |                               4 /      2   |   \6 + x    x *(-5 + 7*x) / |                                 /     2\           4 /      2                                               4 /      2          |                  |                                 /     2\           4 /      2                                               4 /      2          |     |                                 /     2\           4 /      2                                               4 /      2          |                     |                               4 /      2   |                  \6 + x    x *(-5 + 7*x) / |                               4 /      2   |                   |                               4 /      2   ||                                              |                          /           3/4                  2           \     |                               4 /      2   |                                    /     2\           4 /      2                                               4 /      2                            |                               4 /      2   ||                                                            /           3/4                  2           \       |
        |                                                                                           3              ||   /     2\                  3*x *(-5 + 7*x)| |    21           616             6        528*(-5 + 14*x)       132*(-5 + 14*x)    |      \                               \/  6 + x    /       \                               \/  6 + x    /     \                               \/  6 + x    /     \                                  \6 + x /           \6 + x /             \/  6 + x                  \6 + x /                        \/  6 + x                         \/  6 + x                                                         /                               \                               \/  6 + x    /                             \                                 \6 + x /           \/  6 + x                                                \/  6 + x           /                  \                                 \6 + x /           \/  6 + x                                                \/  6 + x           /     \                                 \6 + x /           \/  6 + x                                                \/  6 + x           /                     \                               \/  6 + x    /                                            \                               \/  6 + x    /                   \                               \/  6 + x    /|        2                                     |/  3      22*(-5 + 14*x)\ |   /     2\                  3*x *(-5 + 7*x)|     \                               \/  6 + x    /                                    \6 + x /           \/  6 + x                                                \/  6 + x                             \                               \/  6 + x    /|      /          /     2           2   \                  \ |   /     2\                  3*x *(-5 + 7*x)|       |
        |                                                                                        cos (x)*(2 + 3*x)*||22*\6 + x /   *(-5 + 14*x) + ---------------|*|--------- - ------------- - ----------- + ---------------- + ----------------------| + ------------------------------------------------- - -------------------------------------------------- - ------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------- + --------------------------------------------------------------------------------------- + --------------------------------------------------------------|   3*cos (x)*(-3*cos(x) + 7*(2 + 3*x)*sin(x))*||------ + --------------|*|22*\6 + x /   *(-5 + 14*x) + ---------------| + ------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------|   21*\(2 + 3*x)*\- cos (x) + 6*sin (x)/ - 6*cos(x)*sin(x)/*|22*\6 + x /   *(-5 + 14*x) + ---------------|*cos(x)|
        |                                                                                                          ||                                  ________  | |        2    3               2 /     2\     4           2     2            /     2\|                               2                                          3                                                    2 /     2\                                                                                                                                       4           2                                                                                                                                                         2                                                                                                              2                                                                                                                                                         4           2                                                                                                                              2            /     2\                                                                                    4           2                                                                  2                                                                        2            /     2\                    |                                              ||     2    2            | |                                  ________  |                             2                                                                                   2                                                                                                 2                                   |                                                            |                                  ________  |       |
        |  /    /     2           2   \                    /        2            2   \       \                     ||                               4 /      2   | |/     2\    x *(-5 + 7*x)   x *\6 + x /    x *(-5 + 7*x)     x *(-5 + 7*x)*\6 + x /|                       /     2\                                          x *(-5 + 7*x)                                        x *\6 + x /                                                                                                                                      x *(-5 + 7*x)                                                                                                                                                     6 + x                                                                                                              x *(-5 + 7*x)                                                                                                                                             x *(-5 + 7*x)                                                                                                                              x *(-5 + 7*x)*\6 + x /                                                                                   x *(-5 + 7*x)                                                                  x *(-5 + 7*x)                                                            x *(-5 + 7*x)*\6 + x /                    |                                              |\6 + x    x *(-5 + 7*x) / |                               4 /      2   |                        6 + x                                                                                   x *(-5 + 7*x)                                                                                     x *(-5 + 7*x)                        |                                                            |                               4 /      2   |       |
   4    |7*\- 9*\- cos (x) + 6*sin (x)/*cos(x) + (2 + 3*x)*\- 19*cos (x) + 30*sin (x)/*sin(x)/                     \\                               \/  6 + x    / \\6 + x /                                                                           /                       \6 + x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     /                                              \                          \                               \/  6 + x    /                                                                                                                                                                                                                                                       /                                                            \                               \/  6 + x    /       |
cos (x)*|------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------|
        |                                              3/4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      3/2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             3/2                                                                                                                                                                                                                                             3/2                                          |
        |                                      /     2\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /     2\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        /     2\                                                                                                                                                                                                                           2            /     2\                                             |
        \                                    x*\6 + x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    8*(-5 + 7*x)*\6 + x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         4*x*(-5 + 7*x)*\6 + x /                                                                                                                                                                                                                        2*x *(-5 + 7*x)*\6 + x /                                             /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                10           11                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               x  *(-5 + 7*x)
((3x+2)((3x2(7x−5)x2+64+22(14x−5)(x2+6)34)(21(x2+6)2−6x2(x2+6)+132(14x−5)x2(7x−5)(x2+6)−616x3(7x−5)+528(14x−5)2x4(7x−5)2)+3(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)(3x2+6+22(14x−5)x2(7x−5))x2+6+30(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)(x2+6)2−6(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)x2(x2+6)+22(14x−5)(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)(3x2+6+22(14x−5)x2(7x−5))x2(7x−5)+264(14x−5)(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)x2(7x−5)(x2+6)−(3x2+6+22(14x−5)x2(7x−5))(−3x4(7x−5)2(x2+6)54+6x2(7x−5)2x2+64+132x2(7x−5)(14x−5)x2+64+616x(7x−5)(x2+6)34+440(14x−5)2(x2+6)34)x2(7x−5)−9(−3x4(7x−5)2(x2+6)54+6x2(7x−5)2x2+64+132x2(7x−5)(14x−5)x2+64+616x(7x−5)(x2+6)34+440(14x−5)2(x2+6)34)x2(7x−5)(x2+6)−616(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)x3(7x−5)+1012(14x−5)2(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)x4(7x−5)2−66(14x−5)(−3x4(7x−5)2(x2+6)54+6x2(7x−5)2x2+64+132x2(7x−5)(14x−5)x2+64+616x(7x−5)(x2+6)34+440(14x−5)2(x2+6)34)x4(7x−5)2+3(5x6(7x−5)3(x2+6)94−6x4(7x−5)3(x2+6)54−66x4(7x−5)2(14x−5)(x2+6)54+1848x3(7x−5)2x2+64+132x2(7x−5)2(14x−5)x2+64+1320x2(7x−5)(14x−5)2x2+64+12320x(7x−5)(14x−5)(x2+6)34+2640(14x−5)3(x2+6)34)x4(7x−5)2)cos⁡3(x)8(7x−5)(x2+6)32+7((3x+2)(30sin⁡2(x)−19cos⁡2(x))sin⁡(x)−9(6sin⁡2(x)−cos⁡2(x))cos⁡(x))x(x2+6)34+3(7(3x+2)sin⁡(x)−3cos⁡(x))((3x2(7x−5)x2+64+22(14x−5)(x2+6)34)(3x2+6+22(14x−5)x2(7x−5))+3(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)x2+6+22(14x−5)(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)x2(7x−5)−−3x4(7x−5)2(x2+6)54+6x2(7x−5)2x2+64+132x2(7x−5)(14x−5)x2+64+616x(7x−5)(x2+6)34+440(14x−5)2(x2+6)34x2(7x−5))cos⁡2(x)4x(7x−5)(x2+6)32+21((3x+2)(6sin⁡2(x)−cos⁡2(x))−6sin⁡(x)cos⁡(x))(3x2(7x−5)x2+64+22(14x−5)(x2+6)34)cos⁡(x)2x2(7x−5)(x2+6)32)cos⁡4(x)x10(7x−5)11\frac{\left(\frac{\left(3 x + 2\right) \left(\left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right) \left(\frac{21}{\left(x^{2} + 6\right)^{2}} - \frac{6}{x^{2} \left(x^{2} + 6\right)} + \frac{132 \left(14 x - 5\right)}{x^{2} \left(7 x - 5\right) \left(x^{2} + 6\right)} - \frac{616}{x^{3} \left(7 x - 5\right)} + \frac{528 \left(14 x - 5\right)^{2}}{x^{4} \left(7 x - 5\right)^{2}}\right) + \frac{3 \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right) \left(\frac{3}{x^{2} + 6} + \frac{22 \left(14 x - 5\right)}{x^{2} \left(7 x - 5\right)}\right)}{x^{2} + 6} + \frac{30 \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{\left(x^{2} + 6\right)^{2}} - \frac{6 \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{2} \left(x^{2} + 6\right)} + \frac{22 \left(14 x - 5\right) \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right) \left(\frac{3}{x^{2} + 6} + \frac{22 \left(14 x - 5\right)}{x^{2} \left(7 x - 5\right)}\right)}{x^{2} \left(7 x - 5\right)} + \frac{264 \left(14 x - 5\right) \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{2} \left(7 x - 5\right) \left(x^{2} + 6\right)} - \frac{\left(\frac{3}{x^{2} + 6} + \frac{22 \left(14 x - 5\right)}{x^{2} \left(7 x - 5\right)}\right) \left(- \frac{3 x^{4} \left(7 x - 5\right)^{2}}{\left(x^{2} + 6\right)^{\frac{5}{4}}} + \frac{6 x^{2} \left(7 x - 5\right)^{2}}{\sqrt[4]{x^{2} + 6}} + \frac{132 x^{2} \left(7 x - 5\right) \left(14 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 616 x \left(7 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}} + 440 \left(14 x - 5\right)^{2} \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{2} \left(7 x - 5\right)} - \frac{9 \left(- \frac{3 x^{4} \left(7 x - 5\right)^{2}}{\left(x^{2} + 6\right)^{\frac{5}{4}}} + \frac{6 x^{2} \left(7 x - 5\right)^{2}}{\sqrt[4]{x^{2} + 6}} + \frac{132 x^{2} \left(7 x - 5\right) \left(14 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 616 x \left(7 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}} + 440 \left(14 x - 5\right)^{2} \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{2} \left(7 x - 5\right) \left(x^{2} + 6\right)} - \frac{616 \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{3} \left(7 x - 5\right)} + \frac{1012 \left(14 x - 5\right)^{2} \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{4} \left(7 x - 5\right)^{2}} - \frac{66 \left(14 x - 5\right) \left(- \frac{3 x^{4} \left(7 x - 5\right)^{2}}{\left(x^{2} + 6\right)^{\frac{5}{4}}} + \frac{6 x^{2} \left(7 x - 5\right)^{2}}{\sqrt[4]{x^{2} + 6}} + \frac{132 x^{2} \left(7 x - 5\right) \left(14 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 616 x \left(7 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}} + 440 \left(14 x - 5\right)^{2} \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{4} \left(7 x - 5\right)^{2}} + \frac{3 \left(\frac{5 x^{6} \left(7 x - 5\right)^{3}}{\left(x^{2} + 6\right)^{\frac{9}{4}}} - \frac{6 x^{4} \left(7 x - 5\right)^{3}}{\left(x^{2} + 6\right)^{\frac{5}{4}}} - \frac{66 x^{4} \left(7 x - 5\right)^{2} \left(14 x - 5\right)}{\left(x^{2} + 6\right)^{\frac{5}{4}}} + \frac{1848 x^{3} \left(7 x - 5\right)^{2}}{\sqrt[4]{x^{2} + 6}} + \frac{132 x^{2} \left(7 x - 5\right)^{2} \left(14 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + \frac{1320 x^{2} \left(7 x - 5\right) \left(14 x - 5\right)^{2}}{\sqrt[4]{x^{2} + 6}} + 12320 x \left(7 x - 5\right) \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}} + 2640 \left(14 x - 5\right)^{3} \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{4} \left(7 x - 5\right)^{2}}\right) \cos^{3}{\left(x \right)}}{8 \left(7 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{2}}} + \frac{7 \left(\left(3 x + 2\right) \left(30 \sin^{2}{\left(x \right)} - 19 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} - 9 \left(6 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}\right)}{x \left(x^{2} + 6\right)^{\frac{3}{4}}} + \frac{3 \left(7 \left(3 x + 2\right) \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right) \left(\left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right) \left(\frac{3}{x^{2} + 6} + \frac{22 \left(14 x - 5\right)}{x^{2} \left(7 x - 5\right)}\right) + \frac{3 \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{2} + 6} + \frac{22 \left(14 x - 5\right) \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right)}{x^{2} \left(7 x - 5\right)} - \frac{- \frac{3 x^{4} \left(7 x - 5\right)^{2}}{\left(x^{2} + 6\right)^{\frac{5}{4}}} + \frac{6 x^{2} \left(7 x - 5\right)^{2}}{\sqrt[4]{x^{2} + 6}} + \frac{132 x^{2} \left(7 x - 5\right) \left(14 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 616 x \left(7 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}} + 440 \left(14 x - 5\right)^{2} \left(x^{2} + 6\right)^{\frac{3}{4}}}{x^{2} \left(7 x - 5\right)}\right) \cos^{2}{\left(x \right)}}{4 x \left(7 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{2}}} + \frac{21 \left(\left(3 x + 2\right) \left(6 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 6 \sin{\left(x \right)} \cos{\left(x \right)}\right) \left(\frac{3 x^{2} \left(7 x - 5\right)}{\sqrt[4]{x^{2} + 6}} + 22 \left(14 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{4}}\right) \cos{\left(x \right)}}{2 x^{2} \left(7 x - 5\right) \left(x^{2} + 6\right)^{\frac{3}{2}}}\right) \cos^{4}{\left(x \right)}}{x^{10} \left(7 x - 5\right)^{11}}
Simplificar
Gráfico
Derivada de y=((cos(x))^7*(3*x+2))/((x^2+6)^(3/4)*(5*x-7*x*x)^11)
    © Sr Examen – Калькулятор