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Derivada de la función/ sin9x/ y=(sin9x)^x3

Derivada de y=(sin9x)^x3

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

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Solución

Ha introducido [src] 
   x3     
sin  (9*x)
sin⁡x3(9x)\sin^{x_{3}}{\left(9 x \right)} 
sin(9*x)^x3
Solución detallada

  1. ∂∂x3sin⁡x3(9x)=log⁡(sin⁡(9x))sin⁡x3(9x)\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⁡(sin⁡(9x))sin⁡x3(9x)\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⁡(sin⁡(9x))sin⁡x3(9x)\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⁡(sin⁡(9x))2sin⁡x3(9x)\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⁡(sin⁡(9x))3sin⁡x3(9x)\log{\left(\sin{\left(9 x \right)} \right)}^{3} \sin^{x_{3}}{\left(9 x \right)}
Simplificar
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