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y=(cos)^(sin3x)
Derivada de la función/ sin3x/ y=(cos)^(sin3x)

Derivada de y=(cos)^(sin3x)

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

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Solución

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

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

    Perola derivada

    (log⁡(sin⁡(3x))+1)sin⁡sin⁡(3x)(3x)\left(\log{\left(\sin{\left(3 x \right)} \right)} + 1\right) \sin^{\sin{\left(3 x \right)}}{\left(3 x \right)}

Respuesta:

(log⁡(sin⁡(3x))+1)sin⁡sin⁡(3x)(3x)\left(\log{\left(\sin{\left(3 x \right)} \right)} + 1\right) \sin^{\sin{\left(3 x \right)}}{\left(3 x \right)}

Gráfica
02468-8-6-4-2-1010-10001000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   sin(3*x)    /                         sin(x)*sin(3*x)\
cos        (x)*|3*cos(3*x)*log(cos(x)) - ---------------|
               \                              cos(x)    /
(3log⁡(cos⁡(x))cos⁡(3x)−sin⁡(x)sin⁡(3x)cos⁡(x))cos⁡sin⁡(3x)(x)\left(3 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(3 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(3 x \right)}}{\cos{\left(x \right)}}\right) \cos^{\sin{\left(3 x \right)}}{\left(x \right)}
Simplificar
Segunda derivada [src] 
               /                                          2                                          2                                \
   sin(3*x)    |/                         sin(x)*sin(3*x)\                                        sin (x)*sin(3*x)   6*cos(3*x)*sin(x)|
cos        (x)*||3*cos(3*x)*log(cos(x)) - ---------------|  - sin(3*x) - 9*log(cos(x))*sin(3*x) - ---------------- - -----------------|
               |\                              cos(x)    /                                               2                 cos(x)     |
               \                                                                                      cos (x)                         /
((3log⁡(cos⁡(x))cos⁡(3x)−sin⁡(x)sin⁡(3x)cos⁡(x))2−9log⁡(cos⁡(x))sin⁡(3x)−sin⁡2(x)sin⁡(3x)cos⁡2(x)−6sin⁡(x)cos⁡(3x)cos⁡(x)−sin⁡(3x))cos⁡sin⁡(3x)(x)\left(\left(3 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(3 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(3 x \right)}}{\cos{\left(x \right)}}\right)^{2} - 9 \log{\left(\cos{\left(x \right)} \right)} \sin{\left(3 x \right)} - \frac{\sin^{2}{\left(x \right)} \sin{\left(3 x \right)}}{\cos^{2}{\left(x \right)}} - \frac{6 \sin{\left(x \right)} \cos{\left(3 x \right)}}{\cos{\left(x \right)}} - \sin{\left(3 x \right)}\right) \cos^{\sin{\left(3 x \right)}}{\left(x \right)}
Simplificar
Tercera derivada [src] 
               /                                          3                                                                                       /                            2                                           \        2                    3                                 \
   sin(3*x)    |/                         sin(x)*sin(3*x)\                                             /                         sin(x)*sin(3*x)\ |                         sin (x)*sin(3*x)   6*cos(3*x)*sin(x)           |   9*sin (x)*cos(3*x)   2*sin (x)*sin(3*x)   25*sin(x)*sin(3*x)|
cos        (x)*||3*cos(3*x)*log(cos(x)) - ---------------|  - 9*cos(3*x) - 27*cos(3*x)*log(cos(x)) - 3*|3*cos(3*x)*log(cos(x)) - ---------------|*|9*log(cos(x))*sin(3*x) + ---------------- + ----------------- + sin(3*x)| - ------------------ - ------------------ + ------------------|
               |\                              cos(x)    /                                             \                              cos(x)    / |                                2                 cos(x)                |           2                    3                  cos(x)      |
               \                                                                                                                                  \                             cos (x)                                    /        cos (x)              cos (x)                           /
((3log⁡(cos⁡(x))cos⁡(3x)−sin⁡(x)sin⁡(3x)cos⁡(x))3−3(3log⁡(cos⁡(x))cos⁡(3x)−sin⁡(x)sin⁡(3x)cos⁡(x))(9log⁡(cos⁡(x))sin⁡(3x)+sin⁡2(x)sin⁡(3x)cos⁡2(x)+6sin⁡(x)cos⁡(3x)cos⁡(x)+sin⁡(3x))−27log⁡(cos⁡(x))cos⁡(3x)−2sin⁡3(x)sin⁡(3x)cos⁡3(x)−9sin⁡2(x)cos⁡(3x)cos⁡2(x)+25sin⁡(x)sin⁡(3x)cos⁡(x)−9cos⁡(3x))cos⁡sin⁡(3x)(x)\left(\left(3 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(3 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(3 x \right)}}{\cos{\left(x \right)}}\right)^{3} - 3 \left(3 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(3 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(3 x \right)}}{\cos{\left(x \right)}}\right) \left(9 \log{\left(\cos{\left(x \right)} \right)} \sin{\left(3 x \right)} + \frac{\sin^{2}{\left(x \right)} \sin{\left(3 x \right)}}{\cos^{2}{\left(x \right)}} + \frac{6 \sin{\left(x \right)} \cos{\left(3 x \right)}}{\cos{\left(x \right)}} + \sin{\left(3 x \right)}\right) - 27 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(3 x \right)} - \frac{2 \sin^{3}{\left(x \right)} \sin{\left(3 x \right)}}{\cos^{3}{\left(x \right)}} - \frac{9 \sin^{2}{\left(x \right)} \cos{\left(3 x \right)}}{\cos^{2}{\left(x \right)}} + \frac{25 \sin{\left(x \right)} \sin{\left(3 x \right)}}{\cos{\left(x \right)}} - 9 \cos{\left(3 x \right)}\right) \cos^{\sin{\left(3 x \right)}}{\left(x \right)}
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Gráfico
Derivada de y=(cos)^(sin3x)
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