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sin(x)^(5*x)
Derivada de la función/ sin(x)/ sin(x)^(5*x)

Derivada de sin(x)^(5*x)

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

Ha introducido [src] 
   5*x   
sin   (x)
sin⁡5x(x)\sin^{5 x}{\left(x \right)} 
sin(x)^(5*x)
Solución detallada

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

    Perola derivada

    (5x)5x(log⁡(5x)+1)\left(5 x\right)^{5 x} \left(\log{\left(5 x \right)} + 1\right)

Respuesta:

(5x)5x(log⁡(5x)+1)\left(5 x\right)^{5 x} \left(\log{\left(5 x \right)} + 1\right)

Gráfica
02468-8-6-4-2-10104e39-2e39
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   5*x    /                5*x*cos(x)\
sin   (x)*|5*log(sin(x)) + ----------|
          \                  sin(x)  /
(5xcos⁡(x)sin⁡(x)+5log⁡(sin⁡(x)))sin⁡5x(x)\left(\frac{5 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 5 \log{\left(\sin{\left(x \right)} \right)}\right) \sin^{5 x}{\left(x \right)}
Simplificar
Segunda derivada [src] 
            /                               2                   2   \
     5*x    |       /x*cos(x)              \    2*cos(x)   x*cos (x)|
5*sin   (x)*|-x + 5*|-------- + log(sin(x))|  + -------- - ---------|
            |       \ sin(x)               /     sin(x)        2    |
            \                                               sin (x) /
5(−x−xcos⁡2(x)sin⁡2(x)+5(xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x)))2+2cos⁡(x)sin⁡(x))sin⁡5x(x)5 \left(- x - \frac{x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + 5 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)^{2} + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{5 x}{\left(x \right)}
Simplificar
Tercera derivada [src] 
            /                                3                               /                    2   \        2             3                \
     5*x    |        /x*cos(x)              \       /x*cos(x)              \ |    2*cos(x)   x*cos (x)|   3*cos (x)   2*x*cos (x)   2*x*cos(x)|
5*sin   (x)*|-3 + 25*|-------- + log(sin(x))|  - 15*|-------- + log(sin(x))|*|x - -------- + ---------| - --------- + ----------- + ----------|
            |        \ sin(x)               /       \ sin(x)               / |     sin(x)        2    |       2            3          sin(x)  |
            \                                                                \                sin (x) /    sin (x)      sin (x)               /
5(2xcos⁡(x)sin⁡(x)+2xcos⁡3(x)sin⁡3(x)+25(xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x)))3−15(xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x)))(x+xcos⁡2(x)sin⁡2(x)−2cos⁡(x)sin⁡(x))−3−3cos⁡2(x)sin⁡2(x))sin⁡5x(x)5 \left(\frac{2 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 x \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + 25 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)^{3} - 15 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right) \left(x + \frac{x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) - 3 - \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{5 x}{\left(x \right)}
Simplificar
Gráfico
Derivada de sin(x)^(5*x)
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