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x^sin(7x)
Derivada de la función/ x^sin/ sin(7x)/ x^sin(7x)

Derivada de x^sin(7x)

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

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Solución

Ha introducido [src] 
 sin(7*x)
x
xsin⁡(7x)x^{\sin{\left(7 x \right)}} 
x^sin(7*x)
Solución detallada

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

    Perola derivada

    (log⁡(sin⁡(7x))+1)sin⁡sin⁡(7x)(7x)\left(\log{\left(\sin{\left(7 x \right)} \right)} + 1\right) \sin^{\sin{\left(7 x \right)}}{\left(7 x \right)}

Respuesta:

(log⁡(sin⁡(7x))+1)sin⁡sin⁡(7x)(7x)\left(\log{\left(\sin{\left(7 x \right)} \right)} + 1\right) \sin^{\sin{\left(7 x \right)}}{\left(7 x \right)}

Gráfica
02468-8-6-4-2-1010-100100
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Trazar el gráfico f'(x)
Primera derivada [src] 
 sin(7*x) /sin(7*x)                    \
x        *|-------- + 7*cos(7*x)*log(x)|
          \   x                        /
xsin⁡(7x)(7log⁡(x)cos⁡(7x)+sin⁡(7x)x)x^{\sin{\left(7 x \right)}} \left(7 \log{\left(x \right)} \cos{\left(7 x \right)} + \frac{\sin{\left(7 x \right)}}{x}\right)
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Segunda derivada [src] 
          /                              2                                              \
 sin(7*x) |/sin(7*x)                    \    sin(7*x)                        14*cos(7*x)|
x        *||-------- + 7*cos(7*x)*log(x)|  - -------- - 49*log(x)*sin(7*x) + -----------|
          |\   x                        /        2                                x     |
          \                                     x                                       /
xsin⁡(7x)((7log⁡(x)cos⁡(7x)+sin⁡(7x)x)2−49log⁡(x)sin⁡(7x)+14cos⁡(7x)x−sin⁡(7x)x2)x^{\sin{\left(7 x \right)}} \left(\left(7 \log{\left(x \right)} \cos{\left(7 x \right)} + \frac{\sin{\left(7 x \right)}}{x}\right)^{2} - 49 \log{\left(x \right)} \sin{\left(7 x \right)} + \frac{14 \cos{\left(7 x \right)}}{x} - \frac{\sin{\left(7 x \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
          /                              3                                                                                                                                                 \
 sin(7*x) |/sin(7*x)                    \                          147*sin(7*x)   21*cos(7*x)     /sin(7*x)                    \ /sin(7*x)   14*cos(7*x)                     \   2*sin(7*x)|
x        *||-------- + 7*cos(7*x)*log(x)|  - 343*cos(7*x)*log(x) - ------------ - ----------- - 3*|-------- + 7*cos(7*x)*log(x)|*|-------- - ----------- + 49*log(x)*sin(7*x)| + ----------|
          |\   x                        /                               x               2         \   x                        / |    2           x                          |        3    |
          \                                                                            x                                         \   x                                       /       x     /
xsin⁡(7x)((7log⁡(x)cos⁡(7x)+sin⁡(7x)x)3−3(7log⁡(x)cos⁡(7x)+sin⁡(7x)x)(49log⁡(x)sin⁡(7x)−14cos⁡(7x)x+sin⁡(7x)x2)−343log⁡(x)cos⁡(7x)−147sin⁡(7x)x−21cos⁡(7x)x2+2sin⁡(7x)x3)x^{\sin{\left(7 x \right)}} \left(\left(7 \log{\left(x \right)} \cos{\left(7 x \right)} + \frac{\sin{\left(7 x \right)}}{x}\right)^{3} - 3 \left(7 \log{\left(x \right)} \cos{\left(7 x \right)} + \frac{\sin{\left(7 x \right)}}{x}\right) \left(49 \log{\left(x \right)} \sin{\left(7 x \right)} - \frac{14 \cos{\left(7 x \right)}}{x} + \frac{\sin{\left(7 x \right)}}{x^{2}}\right) - 343 \log{\left(x \right)} \cos{\left(7 x \right)} - \frac{147 \sin{\left(7 x \right)}}{x} - \frac{21 \cos{\left(7 x \right)}}{x^{2}} + \frac{2 \sin{\left(7 x \right)}}{x^{3}}\right)
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Gráfico
Derivada de x^sin(7x)
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