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Derivada de la función/ x^sin/ i*n*x/ x^sin(i*n*x)

Derivada de x^sin(i*n*x)

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

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

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

    Perola derivada

    (log⁡(sin⁡(xin))+1)sin⁡sin⁡(xin)(xin)\left(\log{\left(\sin{\left(x i n \right)} \right)} + 1\right) \sin^{\sin{\left(x i n \right)}}{\left(x i n \right)}

  2. Simplificamos:

    (isinh⁡(nx))isinh⁡(nx)(log⁡(isinh⁡(nx))+1)\left(i \sinh{\left(n x \right)}\right)^{i \sinh{\left(n x \right)}} \left(\log{\left(i \sinh{\left(n x \right)} \right)} + 1\right)

Respuesta:

(isinh⁡(nx))isinh⁡(nx)(log⁡(isinh⁡(nx))+1)\left(i \sinh{\left(n x \right)}\right)^{i \sinh{\left(n x \right)}} \left(\log{\left(i \sinh{\left(n x \right)} \right)} + 1\right)

Primera derivada [src] 
 sin(I*n*x) /sin(I*n*x)                       \
x          *|---------- + I*n*cosh(n*x)*log(x)|
            \    x                            /
xsin⁡(xin)(inlog⁡(x)cosh⁡(nx)+sin⁡(xin)x)x^{\sin{\left(x i n \right)}} \left(i n \log{\left(x \right)} \cosh{\left(n x \right)} + \frac{\sin{\left(x i n \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
             /                                  2                                                        \
 I*sinh(n*x) |  /sinh(n*x)                     \      /  sinh(n*x)    2                    2*n*cosh(n*x)\|
x           *|- |--------- + n*cosh(n*x)*log(x)|  + I*|- --------- + n *log(x)*sinh(n*x) + -------------||
             |  \    x                         /      |       2                                  x      ||
             \                                        \      x                                          //
xisinh⁡(nx)(−(nlog⁡(x)cosh⁡(nx)+sinh⁡(nx)x)2+i(n2log⁡(x)sinh⁡(nx)+2ncosh⁡(nx)x−sinh⁡(nx)x2))x^{i \sinh{\left(n x \right)}} \left(- \left(n \log{\left(x \right)} \cosh{\left(n x \right)} + \frac{\sinh{\left(n x \right)}}{x}\right)^{2} + i \left(n^{2} \log{\left(x \right)} \sinh{\left(n x \right)} + \frac{2 n \cosh{\left(n x \right)}}{x} - \frac{\sinh{\left(n x \right)}}{x^{2}}\right)\right)
Simplificar
Tercera derivada [src] 
             /  /                                                       2          \                                     3                                                                                         \
 I*sinh(n*x) |  |2*sinh(n*x)    3                    3*n*cosh(n*x)   3*n *sinh(n*x)|     /sinh(n*x)                     \      /sinh(n*x)                     \ /  sinh(n*x)    2                    2*n*cosh(n*x)\|
x           *|I*|----------- + n *cosh(n*x)*log(x) - ------------- + --------------| - I*|--------- + n*cosh(n*x)*log(x)|  - 3*|--------- + n*cosh(n*x)*log(x)|*|- --------- + n *log(x)*sinh(n*x) + -------------||
             |  |      3                                    2              x       |     \    x                         /      \    x                         / |       2                                  x      ||
             \  \     x                                    x                       /                                                                            \      x                                          //
xisinh⁡(nx)(−i(nlog⁡(x)cosh⁡(nx)+sinh⁡(nx)x)3−3(nlog⁡(x)cosh⁡(nx)+sinh⁡(nx)x)(n2log⁡(x)sinh⁡(nx)+2ncosh⁡(nx)x−sinh⁡(nx)x2)+i(n3log⁡(x)cosh⁡(nx)+3n2sinh⁡(nx)x−3ncosh⁡(nx)x2+2sinh⁡(nx)x3))x^{i \sinh{\left(n x \right)}} \left(- i \left(n \log{\left(x \right)} \cosh{\left(n x \right)} + \frac{\sinh{\left(n x \right)}}{x}\right)^{3} - 3 \left(n \log{\left(x \right)} \cosh{\left(n x \right)} + \frac{\sinh{\left(n x \right)}}{x}\right) \left(n^{2} \log{\left(x \right)} \sinh{\left(n x \right)} + \frac{2 n \cosh{\left(n x \right)}}{x} - \frac{\sinh{\left(n x \right)}}{x^{2}}\right) + i \left(n^{3} \log{\left(x \right)} \cosh{\left(n x \right)} + \frac{3 n^{2} \sinh{\left(n x \right)}}{x} - \frac{3 n \cosh{\left(n x \right)}}{x^{2}} + \frac{2 \sinh{\left(n x \right)}}{x^{3}}\right)\right)
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