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y=(sin2x)^(x-1)
Derivada de la función/ sin2x/ (x-1)/ y=(sin2x)^(x-1)

Derivada de y=(sin2x)^(x-1)

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

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Solución

Ha introducido [src] 
   x - 1     
sin     (2*x)
$$\sin^{x - 1}{\left(2 x \right)}$$ 
sin(2*x)^(x - 1)
Solución detallada

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

    Perola derivada

  2. Simplificamos:

Respuesta:

Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   x - 1      /2*(x - 1)*cos(2*x)                \
sin     (2*x)*|------------------ + log(sin(2*x))|
              \     sin(2*x)                     /
$$\left(\frac{2 \left(x - 1\right) \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \log{\left(\sin{\left(2 x \right)} \right)}\right) \sin^{x - 1}{\left(2 x \right)}$$
Simplificar
Segunda derivada [src] 
               /                                         2                           2              \
   -1 + x      |    /2*(-1 + x)*cos(2*x)                \          4*cos(2*x)   4*cos (2*x)*(-1 + x)|
sin      (2*x)*|4 + |------------------- + log(sin(2*x))|  - 4*x + ---------- - --------------------|
               |    \      sin(2*x)                     /           sin(2*x)            2           |
               \                                                                     sin (2*x)      /
$$\left(- 4 x - \frac{4 \left(x - 1\right) \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} + \left(\frac{2 \left(x - 1\right) \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \log{\left(\sin{\left(2 x \right)} \right)}\right)^{2} + 4 + \frac{4 \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right) \sin^{x - 1}{\left(2 x \right)}$$
Simplificar
Tercera derivada [src] 
               /                                           3         2                                                 /                       2              \         3                                     \
   -1 + x      |      /2*(-1 + x)*cos(2*x)                \    12*cos (2*x)      /2*(-1 + x)*cos(2*x)                \ |         cos(2*x)   cos (2*x)*(-1 + x)|   16*cos (2*x)*(-1 + x)   16*(-1 + x)*cos(2*x)|
sin      (2*x)*|-12 + |------------------- + log(sin(2*x))|  - ------------ - 12*|------------------- + log(sin(2*x))|*|-1 + x - -------- + ------------------| + --------------------- + --------------------|
               |      \      sin(2*x)                     /        2             \      sin(2*x)                     / |         sin(2*x)          2          |            3                    sin(2*x)      |
               \                                                sin (2*x)                                              \                        sin (2*x)     /         sin (2*x)                             /
$$\left(\frac{16 \left(x - 1\right) \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{16 \left(x - 1\right) \cos^{3}{\left(2 x \right)}}{\sin^{3}{\left(2 x \right)}} + \left(\frac{2 \left(x - 1\right) \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \log{\left(\sin{\left(2 x \right)} \right)}\right)^{3} - 12 \left(\frac{2 \left(x - 1\right) \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \log{\left(\sin{\left(2 x \right)} \right)}\right) \left(x + \frac{\left(x - 1\right) \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} - 1 - \frac{\cos{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right) - 12 - \frac{12 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) \sin^{x - 1}{\left(2 x \right)}$$
Simplificar
Gráfico
Derivada de y=(sin2x)^(x-1)
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