Derivada de y=(cos(3x))^sin2x

Ha introducido [src]

   sin(2*x)     
cos        (3*x)

$$\cos^{\sin{\left(2 x \right)}}{\left(3 x \right)}$$

cos(3*x)^sin(2*x)

Solución detallada

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

Perola derivada

$\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \right)}$

Respuesta:

$\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \right)}$

Gráfica

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Primera derivada [src]

   sin(2*x)      /                           3*sin(2*x)*sin(3*x)\
cos        (3*x)*|2*cos(2*x)*log(cos(3*x)) - -------------------|
                 \                                 cos(3*x)     /

$$\left(2 \log{\left(\cos{\left(3 x \right)} \right)} \cos{\left(2 x \right)} - \frac{3 \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}\right) \cos^{\sin{\left(2 x \right)}}{\left(3 x \right)}$$

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Segunda derivada [src]

                 /                                                2                                                                       2              \
   sin(2*x)      |/                           3*sin(2*x)*sin(3*x)\                                            12*cos(2*x)*sin(3*x)   9*sin (3*x)*sin(2*x)|
cos        (3*x)*||2*cos(2*x)*log(cos(3*x)) - -------------------|  - 9*sin(2*x) - 4*log(cos(3*x))*sin(2*x) - -------------------- - --------------------|
                 |\                                 cos(3*x)     /                                                  cos(3*x)                 2           |
                 \                                                                                                                        cos (3*x)      /

$$\left(\left(2 \log{\left(\cos{\left(3 x \right)} \right)} \cos{\left(2 x \right)} - \frac{3 \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}\right)^{2} - 4 \log{\left(\cos{\left(3 x \right)} \right)} \sin{\left(2 x \right)} - \frac{9 \sin{\left(2 x \right)} \sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} - 9 \sin{\left(2 x \right)} - \frac{12 \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{\cos{\left(3 x \right)}}\right) \cos^{\sin{\left(2 x \right)}}{\left(3 x \right)}$$

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Tercera derivada [src]

                 /                                                3                                                                                               /                                             2                                     \         3                       2                                     \
   sin(2*x)      |/                           3*sin(2*x)*sin(3*x)\                                               /                           3*sin(2*x)*sin(3*x)\ |                                        9*sin (3*x)*sin(2*x)   12*cos(2*x)*sin(3*x)|   54*sin (3*x)*sin(2*x)   54*sin (3*x)*cos(2*x)   18*sin(2*x)*sin(3*x)|
cos        (3*x)*||2*cos(2*x)*log(cos(3*x)) - -------------------|  - 54*cos(2*x) - 8*cos(2*x)*log(cos(3*x)) - 3*|2*cos(2*x)*log(cos(3*x)) - -------------------|*|9*sin(2*x) + 4*log(cos(3*x))*sin(2*x) + -------------------- + --------------------| - --------------------- - --------------------- - --------------------|
                 |\                                 cos(3*x)     /                                               \                                 cos(3*x)     / |                                                2                    cos(3*x)      |            3                       2                    cos(3*x)      |
                 \                                                                                                                                                \                                             cos (3*x)                             /         cos (3*x)               cos (3*x)                             /

$$\left(\left(2 \log{\left(\cos{\left(3 x \right)} \right)} \cos{\left(2 x \right)} - \frac{3 \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}\right)^{3} - 3 \left(2 \log{\left(\cos{\left(3 x \right)} \right)} \cos{\left(2 x \right)} - \frac{3 \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}\right) \left(4 \log{\left(\cos{\left(3 x \right)} \right)} \sin{\left(2 x \right)} + \frac{9 \sin{\left(2 x \right)} \sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} + 9 \sin{\left(2 x \right)} + \frac{12 \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{\cos{\left(3 x \right)}}\right) - 8 \log{\left(\cos{\left(3 x \right)} \right)} \cos{\left(2 x \right)} - \frac{54 \sin{\left(2 x \right)} \sin^{3}{\left(3 x \right)}}{\cos^{3}{\left(3 x \right)}} - \frac{18 \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \frac{54 \sin^{2}{\left(3 x \right)} \cos{\left(2 x \right)}}{\cos^{2}{\left(3 x \right)}} - 54 \cos{\left(2 x \right)}\right) \cos^{\sin{\left(2 x \right)}}{\left(3 x \right)}$$

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Gráfico

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Derivada de y=(cos(3x))^sin2x

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