Derivada de y=(cos4x)^x

Ha introducido [src]

   x     
cos (4*x)

$$\cos^{x}{\left(4 x \right)}$$

cos(4*x)^x

Solución detallada

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Perola derivada

$x^{x} \left(\log{\left(x \right)} + 1\right)$

Respuesta:

$x^{x} \left(\log{\left(x \right)} + 1\right)$

Gráfica

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Trazar el gráfico f'(x)

Primera derivada [src]

   x      /  4*x*sin(4*x)                \
cos (4*x)*|- ------------ + log(cos(4*x))|
          \    cos(4*x)                  /

$$\left(- \frac{4 x \sin{\left(4 x \right)}}{\cos{\left(4 x \right)}} + \log{\left(\cos{\left(4 x \right)} \right)}\right) \cos^{x}{\left(4 x \right)}$$

Simplificar

Segunda derivada [src]

          /                               2                               2     \
   x      |/                 4*x*sin(4*x)\           8*sin(4*x)   16*x*sin (4*x)|
cos (4*x)*||-log(cos(4*x)) + ------------|  - 16*x - ---------- - --------------|
          |\                   cos(4*x)  /            cos(4*x)         2        |
          \                                                         cos (4*x)   /

$$\left(- \frac{16 x \sin^{2}{\left(4 x \right)}}{\cos^{2}{\left(4 x \right)}} - 16 x + \left(\frac{4 x \sin{\left(4 x \right)}}{\cos{\left(4 x \right)}} - \log{\left(\cos{\left(4 x \right)} \right)}\right)^{2} - \frac{8 \sin{\left(4 x \right)}}{\cos{\left(4 x \right)}}\right) \cos^{x}{\left(4 x \right)}$$

Simplificar

Tercera derivada [src]

          /                                     3         2                                           /                        2     \                             3     \
   x      |      /                 4*x*sin(4*x)\    48*sin (4*x)      /                 4*x*sin(4*x)\ |      sin(4*x)   2*x*sin (4*x)|   128*x*sin(4*x)   128*x*sin (4*x)|
cos (4*x)*|-48 - |-log(cos(4*x)) + ------------|  - ------------ + 24*|-log(cos(4*x)) + ------------|*|2*x + -------- + -------------| - -------------- - ---------------|
          |      \                   cos(4*x)  /        2             \                   cos(4*x)  / |      cos(4*x)        2       |      cos(4*x)            3        |
          \                                          cos (4*x)                                        \                   cos (4*x)  /                       cos (4*x)   /

$$\left(- \frac{128 x \sin^{3}{\left(4 x \right)}}{\cos^{3}{\left(4 x \right)}} - \frac{128 x \sin{\left(4 x \right)}}{\cos{\left(4 x \right)}} - \left(\frac{4 x \sin{\left(4 x \right)}}{\cos{\left(4 x \right)}} - \log{\left(\cos{\left(4 x \right)} \right)}\right)^{3} + 24 \left(\frac{4 x \sin{\left(4 x \right)}}{\cos{\left(4 x \right)}} - \log{\left(\cos{\left(4 x \right)} \right)}\right) \left(\frac{2 x \sin^{2}{\left(4 x \right)}}{\cos^{2}{\left(4 x \right)}} + 2 x + \frac{\sin{\left(4 x \right)}}{\cos{\left(4 x \right)}}\right) - \frac{48 \sin^{2}{\left(4 x \right)}}{\cos^{2}{\left(4 x \right)}} - 48\right) \cos^{x}{\left(4 x \right)}$$

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Gráfico

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Expresiones idénticas

Derivada de y=(cos4x)^x

Gráfico:

Definida a trozos:

Solución