Derivada de y=(sin9x)^x3

Ha introducido [src]

   x3     
sin  (9*x)

$$\sin^{x_{3}}{\left(9 x \right)}$$

sin(9*x)^x3

Solución detallada

$\frac{\partial}{\partial x_{3}} \sin^{x_{3}}{\left(9 x \right)} = \log{\left(\sin{\left(9 x \right)} \right)} \sin^{x_{3}}{\left(9 x \right)}$

Respuesta:

$\log{\left(\sin{\left(9 x \right)} \right)} \sin^{x_{3}}{\left(9 x \right)}$

Primera derivada [src]

   x3                   
sin  (9*x)*log(sin(9*x))

$$\log{\left(\sin{\left(9 x \right)} \right)} \sin^{x_{3}}{\left(9 x \right)}$$

Simplificar

Segunda derivada [src]

   2              x3     
log (sin(9*x))*sin  (9*x)

$$\log{\left(\sin{\left(9 x \right)} \right)}^{2} \sin^{x_{3}}{\left(9 x \right)}$$

Simplificar

Tercera derivada [src]

   3              x3     
log (sin(9*x))*sin  (9*x)

$$\log{\left(\sin{\left(9 x \right)} \right)}^{3} \sin^{x_{3}}{\left(9 x \right)}$$

Simplificar