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x^sin(4x)
Derivada de la función/ x^sin/ sin(4x)/ x^sin(4x)

Derivada de x^sin(4x)

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

Ha introducido [src] 
 sin(4*x)
x
xsin⁡(4x)x^{\sin{\left(4 x \right)}} 
x^sin(4*x)
Solución detallada

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

    Perola derivada

    (log⁡(sin⁡(4x))+1)sin⁡sin⁡(4x)(4x)\left(\log{\left(\sin{\left(4 x \right)} \right)} + 1\right) \sin^{\sin{\left(4 x \right)}}{\left(4 x \right)}

Respuesta:

(log⁡(sin⁡(4x))+1)sin⁡sin⁡(4x)(4x)\left(\log{\left(\sin{\left(4 x \right)} \right)} + 1\right) \sin^{\sin{\left(4 x \right)}}{\left(4 x \right)}

Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 sin(4*x) /sin(4*x)                    \
x        *|-------- + 4*cos(4*x)*log(x)|
          \   x                        /
xsin⁡(4x)(4log⁡(x)cos⁡(4x)+sin⁡(4x)x)x^{\sin{\left(4 x \right)}} \left(4 \log{\left(x \right)} \cos{\left(4 x \right)} + \frac{\sin{\left(4 x \right)}}{x}\right)
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Segunda derivada [src] 
          /                              2                                             \
 sin(4*x) |/sin(4*x)                    \    sin(4*x)                        8*cos(4*x)|
x        *||-------- + 4*cos(4*x)*log(x)|  - -------- - 16*log(x)*sin(4*x) + ----------|
          |\   x                        /        2                               x     |
          \                                     x                                      /
xsin⁡(4x)((4log⁡(x)cos⁡(4x)+sin⁡(4x)x)2−16log⁡(x)sin⁡(4x)+8cos⁡(4x)x−sin⁡(4x)x2)x^{\sin{\left(4 x \right)}} \left(\left(4 \log{\left(x \right)} \cos{\left(4 x \right)} + \frac{\sin{\left(4 x \right)}}{x}\right)^{2} - 16 \log{\left(x \right)} \sin{\left(4 x \right)} + \frac{8 \cos{\left(4 x \right)}}{x} - \frac{\sin{\left(4 x \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
          /                              3                                                                                                                                              \
 sin(4*x) |/sin(4*x)                    \                         48*sin(4*x)   12*cos(4*x)     /sin(4*x)                    \ /sin(4*x)   8*cos(4*x)                     \   2*sin(4*x)|
x        *||-------- + 4*cos(4*x)*log(x)|  - 64*cos(4*x)*log(x) - ----------- - ----------- - 3*|-------- + 4*cos(4*x)*log(x)|*|-------- - ---------- + 16*log(x)*sin(4*x)| + ----------|
          |\   x                        /                              x              2         \   x                        / |    2          x                          |        3    |
          \                                                                          x                                         \   x                                      /       x     /
xsin⁡(4x)((4log⁡(x)cos⁡(4x)+sin⁡(4x)x)3−3(4log⁡(x)cos⁡(4x)+sin⁡(4x)x)(16log⁡(x)sin⁡(4x)−8cos⁡(4x)x+sin⁡(4x)x2)−64log⁡(x)cos⁡(4x)−48sin⁡(4x)x−12cos⁡(4x)x2+2sin⁡(4x)x3)x^{\sin{\left(4 x \right)}} \left(\left(4 \log{\left(x \right)} \cos{\left(4 x \right)} + \frac{\sin{\left(4 x \right)}}{x}\right)^{3} - 3 \left(4 \log{\left(x \right)} \cos{\left(4 x \right)} + \frac{\sin{\left(4 x \right)}}{x}\right) \left(16 \log{\left(x \right)} \sin{\left(4 x \right)} - \frac{8 \cos{\left(4 x \right)}}{x} + \frac{\sin{\left(4 x \right)}}{x^{2}}\right) - 64 \log{\left(x \right)} \cos{\left(4 x \right)} - \frac{48 \sin{\left(4 x \right)}}{x} - \frac{12 \cos{\left(4 x \right)}}{x^{2}} + \frac{2 \sin{\left(4 x \right)}}{x^{3}}\right)
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Gráfico
Derivada de x^sin(4x)
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