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y=cos2x^sinx
Derivada de la función/ x^sin/ y=cos/ cos2x/ y=cos2x^sinx

Derivada de y=cos2x^sinx

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

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Definida a trozos:

Solución

Ha introducido [src] 
   sin(x)     
cos      (2*x)
cos⁡sin⁡(x)(2x)\cos^{\sin{\left(x \right)}}{\left(2 x \right)} 
cos(2*x)^sin(x)
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-10050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   sin(x)      /                       2*sin(x)*sin(2*x)\
cos      (2*x)*|cos(x)*log(cos(2*x)) - -----------------|
               \                            cos(2*x)    /
(log⁡(cos⁡(2x))cos⁡(x)−2sin⁡(x)sin⁡(2x)cos⁡(2x))cos⁡sin⁡(x)(2x)\left(\log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}\right) \cos^{\sin{\left(x \right)}}{\left(2 x \right)}
Simplificar
Segunda derivada [src] 
               /                                          2                                                              2            \
   sin(x)      |/                       2*sin(x)*sin(2*x)\                                      4*cos(x)*sin(2*x)   4*sin (2*x)*sin(x)|
cos      (2*x)*||cos(x)*log(cos(2*x)) - -----------------|  - 4*sin(x) - log(cos(2*x))*sin(x) - ----------------- - ------------------|
               |\                            cos(2*x)    /                                           cos(2*x)              2          |
               \                                                                                                        cos (2*x)     /
((log⁡(cos⁡(2x))cos⁡(x)−2sin⁡(x)sin⁡(2x)cos⁡(2x))2−log⁡(cos⁡(2x))sin⁡(x)−4sin⁡(x)sin⁡2(2x)cos⁡2(2x)−4sin⁡(x)−4sin⁡(2x)cos⁡(x)cos⁡(2x))cos⁡sin⁡(x)(2x)\left(\left(\log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}\right)^{2} - \log{\left(\cos{\left(2 x \right)} \right)} \sin{\left(x \right)} - \frac{4 \sin{\left(x \right)} \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} - 4 \sin{\left(x \right)} - \frac{4 \sin{\left(2 x \right)} \cos{\left(x \right)}}{\cos{\left(2 x \right)}}\right) \cos^{\sin{\left(x \right)}}{\left(2 x \right)}
Simplificar
Tercera derivada [src] 
               /                                          3                                                                                   /                                                           2            \         3                     2                                 \
   sin(x)      |/                       2*sin(x)*sin(2*x)\                                         /                       2*sin(x)*sin(2*x)\ |                                  4*cos(x)*sin(2*x)   4*sin (2*x)*sin(x)|   16*sin (2*x)*sin(x)   12*sin (2*x)*cos(x)   10*sin(x)*sin(2*x)|
cos      (2*x)*||cos(x)*log(cos(2*x)) - -----------------|  - 12*cos(x) - cos(x)*log(cos(2*x)) - 3*|cos(x)*log(cos(2*x)) - -----------------|*|4*sin(x) + log(cos(2*x))*sin(x) + ----------------- + ------------------| - ------------------- - ------------------- - ------------------|
               |\                            cos(2*x)    /                                         \                            cos(2*x)    / |                                       cos(2*x)              2          |           3                     2                  cos(2*x)     |
               \                                                                                                                              \                                                          cos (2*x)     /        cos (2*x)             cos (2*x)                          /
((log⁡(cos⁡(2x))cos⁡(x)−2sin⁡(x)sin⁡(2x)cos⁡(2x))3−3(log⁡(cos⁡(2x))cos⁡(x)−2sin⁡(x)sin⁡(2x)cos⁡(2x))(log⁡(cos⁡(2x))sin⁡(x)+4sin⁡(x)sin⁡2(2x)cos⁡2(2x)+4sin⁡(x)+4sin⁡(2x)cos⁡(x)cos⁡(2x))−log⁡(cos⁡(2x))cos⁡(x)−16sin⁡(x)sin⁡3(2x)cos⁡3(2x)−10sin⁡(x)sin⁡(2x)cos⁡(2x)−12sin⁡2(2x)cos⁡(x)cos⁡2(2x)−12cos⁡(x))cos⁡sin⁡(x)(2x)\left(\left(\log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}\right)^{3} - 3 \left(\log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}\right) \left(\log{\left(\cos{\left(2 x \right)} \right)} \sin{\left(x \right)} + \frac{4 \sin{\left(x \right)} \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + 4 \sin{\left(x \right)} + \frac{4 \sin{\left(2 x \right)} \cos{\left(x \right)}}{\cos{\left(2 x \right)}}\right) - \log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{16 \sin{\left(x \right)} \sin^{3}{\left(2 x \right)}}{\cos^{3}{\left(2 x \right)}} - \frac{10 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} - \frac{12 \sin^{2}{\left(2 x \right)} \cos{\left(x \right)}}{\cos^{2}{\left(2 x \right)}} - 12 \cos{\left(x \right)}\right) \cos^{\sin{\left(x \right)}}{\left(2 x \right)}
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Gráfico
Derivada de y=cos2x^sinx
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