Derivada de x^sin(x^6)

Ha introducido [src]

    / 6\
 sin\x /
x

x^{\sin{\left(x^{6} \right)}}

x^sin(x^6)

Solución detallada

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

Perola derivada

$\left(\log{\left(\sin{\left(x^{6} \right)} \right)} + 1\right) \sin^{\sin{\left(x^{6} \right)}}{\left(x^{6} \right)}$

Respuesta:

$\left(\log{\left(\sin{\left(x^{6} \right)} \right)} + 1\right) \sin^{\sin{\left(x^{6} \right)}}{\left(x^{6} \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

    / 6\ /   / 6\                      \
 sin\x / |sin\x /      5    / 6\       |
x       *|------- + 6*x *cos\x /*log(x)|
         \   x                         /

x^{\sin{\left(x^{6} \right)}} \left(6 x^{5} \log{\left(x \right)} \cos{\left(x^{6} \right)} + \frac{\sin{\left(x^{6} \right)}}{x}\right)

Simplificar

Segunda derivada [src]

         /                               2                                                                         \
    / 6\ |/   / 6\                      \       / 6\                                                               |
 sin\x / ||sin\x /      5    / 6\       |    sin\x /       4    / 6\       10           / 6\       4    / 6\       |
x       *||------- + 6*x *cos\x /*log(x)|  - ------- + 12*x *cos\x / - 36*x  *log(x)*sin\x / + 30*x *cos\x /*log(x)|
         |\   x                         /        2                                                                 |
         \                                      x                                                                  /

x^{\sin{\left(x^{6} \right)}} \left(- 36 x^{10} \log{\left(x \right)} \sin{\left(x^{6} \right)} + 30 x^{4} \log{\left(x \right)} \cos{\left(x^{6} \right)} + 12 x^{4} \cos{\left(x^{6} \right)} + \left(6 x^{5} \log{\left(x \right)} \cos{\left(x^{6} \right)} + \frac{\sin{\left(x^{6} \right)}}{x}\right)^{2} - \frac{\sin{\left(x^{6} \right)}}{x^{2}}\right)

Simplificar

Tercera derivada [src]

         /                               3                                                                                                                                                                                                                                   \
    / 6\ |/   / 6\                      \                       /   / 6\                      \ /   / 6\                                                               \        / 6\                                                                                         |
 sin\x / ||sin\x /      5    / 6\       |         9    / 6\     |sin\x /      5    / 6\       | |sin\x /       4    / 6\       4    / 6\              10           / 6\|   2*sin\x /       3    / 6\        9           / 6\        15    / 6\               3    / 6\       |
x       *||------- + 6*x *cos\x /*log(x)|  - 108*x *sin\x / - 3*|------- + 6*x *cos\x /*log(x)|*|------- - 12*x *cos\x / - 30*x *cos\x /*log(x) + 36*x  *log(x)*sin\x /| + --------- + 72*x *cos\x / - 540*x *log(x)*sin\x / - 216*x  *cos\x /*log(x) + 120*x *cos\x /*log(x)|
         |\   x                         /                       \   x                         / |    2                                                                 |        3                                                                                            |
         \                                                                                      \   x                                                                  /       x                                                                                             /

x^{\sin{\left(x^{6} \right)}} \left(- 216 x^{15} \log{\left(x \right)} \cos{\left(x^{6} \right)} - 540 x^{9} \log{\left(x \right)} \sin{\left(x^{6} \right)} - 108 x^{9} \sin{\left(x^{6} \right)} + 120 x^{3} \log{\left(x \right)} \cos{\left(x^{6} \right)} + 72 x^{3} \cos{\left(x^{6} \right)} + \left(6 x^{5} \log{\left(x \right)} \cos{\left(x^{6} \right)} + \frac{\sin{\left(x^{6} \right)}}{x}\right)^{3} - 3 \left(6 x^{5} \log{\left(x \right)} \cos{\left(x^{6} \right)} + \frac{\sin{\left(x^{6} \right)}}{x}\right) \left(36 x^{10} \log{\left(x \right)} \sin{\left(x^{6} \right)} - 30 x^{4} \log{\left(x \right)} \cos{\left(x^{6} \right)} - 12 x^{4} \cos{\left(x^{6} \right)} + \frac{\sin{\left(x^{6} \right)}}{x^{2}}\right) + \frac{2 \sin{\left(x^{6} \right)}}{x^{3}}\right)

Simplificar

Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones con funciones

Derivada de x^sin(x^6)

Gráfico:

Definida a trozos:

Solución