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y=(cos(7x))^sin3x
Derivada de la función/ sin3x/ cos(7x)/ y=(cos(7x))^sin3x

Derivada de y=(cos(7x))^sin3x

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

Ha introducido [src] 
   sin(3*x)     
cos        (7*x)
cos⁡sin⁡(3x)(7x)\cos^{\sin{\left(3 x \right)}}{\left(7 x \right)} 
cos(7*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)
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Primera derivada [src] 
   sin(3*x)      /                           7*sin(3*x)*sin(7*x)\
cos        (7*x)*|3*cos(3*x)*log(cos(7*x)) - -------------------|
                 \                                 cos(7*x)     /
(3log⁡(cos⁡(7x))cos⁡(3x)−7sin⁡(3x)sin⁡(7x)cos⁡(7x))cos⁡sin⁡(3x)(7x)\left(3 \log{\left(\cos{\left(7 x \right)} \right)} \cos{\left(3 x \right)} - \frac{7 \sin{\left(3 x \right)} \sin{\left(7 x \right)}}{\cos{\left(7 x \right)}}\right) \cos^{\sin{\left(3 x \right)}}{\left(7 x \right)}
Simplificar
Segunda derivada [src] 
                 /                                                2                                                  2                                     \
   sin(3*x)      |/                           7*sin(3*x)*sin(7*x)\                                             49*sin (7*x)*sin(3*x)   42*cos(3*x)*sin(7*x)|
cos        (7*x)*||3*cos(3*x)*log(cos(7*x)) - -------------------|  - 49*sin(3*x) - 9*log(cos(7*x))*sin(3*x) - --------------------- - --------------------|
                 |\                                 cos(7*x)     /                                                      2                    cos(7*x)      |
                 \                                                                                                   cos (7*x)                             /
((3log⁡(cos⁡(7x))cos⁡(3x)−7sin⁡(3x)sin⁡(7x)cos⁡(7x))2−9log⁡(cos⁡(7x))sin⁡(3x)−49sin⁡(3x)sin⁡2(7x)cos⁡2(7x)−49sin⁡(3x)−42sin⁡(7x)cos⁡(3x)cos⁡(7x))cos⁡sin⁡(3x)(7x)\left(\left(3 \log{\left(\cos{\left(7 x \right)} \right)} \cos{\left(3 x \right)} - \frac{7 \sin{\left(3 x \right)} \sin{\left(7 x \right)}}{\cos{\left(7 x \right)}}\right)^{2} - 9 \log{\left(\cos{\left(7 x \right)} \right)} \sin{\left(3 x \right)} - \frac{49 \sin{\left(3 x \right)} \sin^{2}{\left(7 x \right)}}{\cos^{2}{\left(7 x \right)}} - 49 \sin{\left(3 x \right)} - \frac{42 \sin{\left(7 x \right)} \cos{\left(3 x \right)}}{\cos{\left(7 x \right)}}\right) \cos^{\sin{\left(3 x \right)}}{\left(7 x \right)}
Simplificar
Tercera derivada [src] 
                 /                                                3                                                                                                 /                                                                      2              \          3                                                2              \
   sin(3*x)      |/                           7*sin(3*x)*sin(7*x)\                                                 /                           7*sin(3*x)*sin(7*x)\ |                                         42*cos(3*x)*sin(7*x)   49*sin (7*x)*sin(3*x)|   686*sin (7*x)*sin(3*x)   497*sin(3*x)*sin(7*x)   441*sin (7*x)*cos(3*x)|
cos        (7*x)*||3*cos(3*x)*log(cos(7*x)) - -------------------|  - 441*cos(3*x) - 27*cos(3*x)*log(cos(7*x)) - 3*|3*cos(3*x)*log(cos(7*x)) - -------------------|*|49*sin(3*x) + 9*log(cos(7*x))*sin(3*x) + -------------------- + ---------------------| - ---------------------- - --------------------- - ----------------------|
                 |\                                 cos(7*x)     /                                                 \                                 cos(7*x)     / |                                               cos(7*x)                  2           |            3                      cos(7*x)                  2            |
                 \                                                                                                                                                  \                                                                      cos (7*x)      /         cos (7*x)                                        cos (7*x)       /
((3log⁡(cos⁡(7x))cos⁡(3x)−7sin⁡(3x)sin⁡(7x)cos⁡(7x))3−3(3log⁡(cos⁡(7x))cos⁡(3x)−7sin⁡(3x)sin⁡(7x)cos⁡(7x))(9log⁡(cos⁡(7x))sin⁡(3x)+49sin⁡(3x)sin⁡2(7x)cos⁡2(7x)+49sin⁡(3x)+42sin⁡(7x)cos⁡(3x)cos⁡(7x))−27log⁡(cos⁡(7x))cos⁡(3x)−686sin⁡(3x)sin⁡3(7x)cos⁡3(7x)−497sin⁡(3x)sin⁡(7x)cos⁡(7x)−441sin⁡2(7x)cos⁡(3x)cos⁡2(7x)−441cos⁡(3x))cos⁡sin⁡(3x)(7x)\left(\left(3 \log{\left(\cos{\left(7 x \right)} \right)} \cos{\left(3 x \right)} - \frac{7 \sin{\left(3 x \right)} \sin{\left(7 x \right)}}{\cos{\left(7 x \right)}}\right)^{3} - 3 \left(3 \log{\left(\cos{\left(7 x \right)} \right)} \cos{\left(3 x \right)} - \frac{7 \sin{\left(3 x \right)} \sin{\left(7 x \right)}}{\cos{\left(7 x \right)}}\right) \left(9 \log{\left(\cos{\left(7 x \right)} \right)} \sin{\left(3 x \right)} + \frac{49 \sin{\left(3 x \right)} \sin^{2}{\left(7 x \right)}}{\cos^{2}{\left(7 x \right)}} + 49 \sin{\left(3 x \right)} + \frac{42 \sin{\left(7 x \right)} \cos{\left(3 x \right)}}{\cos{\left(7 x \right)}}\right) - 27 \log{\left(\cos{\left(7 x \right)} \right)} \cos{\left(3 x \right)} - \frac{686 \sin{\left(3 x \right)} \sin^{3}{\left(7 x \right)}}{\cos^{3}{\left(7 x \right)}} - \frac{497 \sin{\left(3 x \right)} \sin{\left(7 x \right)}}{\cos{\left(7 x \right)}} - \frac{441 \sin^{2}{\left(7 x \right)} \cos{\left(3 x \right)}}{\cos^{2}{\left(7 x \right)}} - 441 \cos{\left(3 x \right)}\right) \cos^{\sin{\left(3 x \right)}}{\left(7 x \right)}
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Gráfico
Derivada de y=(cos(7x))^sin3x
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