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(cos3x)^x
Derivada de la función/ cos3x/ (cos3x)^x

Derivada de (cos3x)^x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   x     
cos (3*x)
$$\cos^{x}{\left(3 x \right)}$$ 
cos(3*x)^x
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

Respuesta:

Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   x      /  3*x*sin(3*x)                \
cos (3*x)*|- ------------ + log(cos(3*x))|
          \    cos(3*x)                  /
$$\left(- \frac{3 x \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} + \log{\left(\cos{\left(3 x \right)} \right)}\right) \cos^{x}{\left(3 x \right)}$$
Simplificar
Segunda derivada [src] 
          /                               2                             2     \
   x      |/                 3*x*sin(3*x)\          6*sin(3*x)   9*x*sin (3*x)|
cos (3*x)*||-log(cos(3*x)) + ------------|  - 9*x - ---------- - -------------|
          |\                   cos(3*x)  /           cos(3*x)         2       |
          \                                                        cos (3*x)  /
$$\left(- \frac{9 x \sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} - 9 x + \left(\frac{3 x \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \log{\left(\cos{\left(3 x \right)} \right)}\right)^{2} - \frac{6 \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}\right) \cos^{x}{\left(3 x \right)}$$
Simplificar
Tercera derivada [src] 
          /                                     3         2                                          /                          2     \                           3     \
   x      |      /                 3*x*sin(3*x)\    27*sin (3*x)     /                 3*x*sin(3*x)\ |      2*sin(3*x)   3*x*sin (3*x)|   54*x*sin(3*x)   54*x*sin (3*x)|
cos (3*x)*|-27 - |-log(cos(3*x)) + ------------|  - ------------ + 9*|-log(cos(3*x)) + ------------|*|3*x + ---------- + -------------| - ------------- - --------------|
          |      \                   cos(3*x)  /        2            \                   cos(3*x)  / |       cos(3*x)         2       |      cos(3*x)          3        |
          \                                          cos (3*x)                                       \                     cos (3*x)  /                     cos (3*x)   /
$$\left(- \frac{54 x \sin^{3}{\left(3 x \right)}}{\cos^{3}{\left(3 x \right)}} - \frac{54 x \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \left(\frac{3 x \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \log{\left(\cos{\left(3 x \right)} \right)}\right)^{3} + 9 \left(\frac{3 x \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \log{\left(\cos{\left(3 x \right)} \right)}\right) \left(\frac{3 x \sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} + 3 x + \frac{2 \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}\right) - \frac{27 \sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} - 27\right) \cos^{x}{\left(3 x \right)}$$
Simplificar
Gráfico
Derivada de (cos3x)^x
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