Derivada de x^(sin(3x)+5x)

Ha introducido [src]

 sin(3*x) + 5*x
x

$$x^{5 x + \sin{\left(3 x \right)}}$$

x^(sin(3*x) + 5*x)

Solución detallada

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

Perola derivada

$\left(5 x + \sin{\left(3 x \right)}\right)^{5 x + \sin{\left(3 x \right)}} \left(\log{\left(5 x + \sin{\left(3 x \right)} \right)} + 1\right)$
Simplificamos:

$\left(5 x + \sin{\left(3 x \right)}\right)^{5 x + \sin{\left(3 x \right)}} \left(\log{\left(5 x + \sin{\left(3 x \right)} \right)} + 1\right)$

Respuesta:

$\left(5 x + \sin{\left(3 x \right)}\right)^{5 x + \sin{\left(3 x \right)}} \left(\log{\left(5 x + \sin{\left(3 x \right)} \right)} + 1\right)$

Gráfica

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Primera derivada [src]

 sin(3*x) + 5*x /sin(3*x) + 5*x                          \
x              *|-------------- + (5 + 3*cos(3*x))*log(x)|
                \      x                                 /

$$x^{5 x + \sin{\left(3 x \right)}} \left(\left(3 \cos{\left(3 x \right)} + 5\right) \log{\left(x \right)} + \frac{5 x + \sin{\left(3 x \right)}}{x}\right)$$

Simplificar

Segunda derivada [src]

                /                                          2                                                          \
 5*x + sin(3*x) |/5*x + sin(3*x)                          \    5*x + sin(3*x)                       2*(5 + 3*cos(3*x))|
x              *||-------------- + (5 + 3*cos(3*x))*log(x)|  - -------------- - 9*log(x)*sin(3*x) + ------------------|
                |\      x                                 /           2                                     x         |
                \                                                    x                                                /

$$x^{5 x + \sin{\left(3 x \right)}} \left(\left(\left(3 \cos{\left(3 x \right)} + 5\right) \log{\left(x \right)} + \frac{5 x + \sin{\left(3 x \right)}}{x}\right)^{2} - 9 \log{\left(x \right)} \sin{\left(3 x \right)} + \frac{2 \left(3 \cos{\left(3 x \right)} + 5\right)}{x} - \frac{5 x + \sin{\left(3 x \right)}}{x^{2}}\right)$$

Simplificar

Tercera derivada [src]

                /                                          3                                                                                                                                                                                      \
 5*x + sin(3*x) |/5*x + sin(3*x)                          \    27*sin(3*x)                        3*(5 + 3*cos(3*x))     /5*x + sin(3*x)                          \ /5*x + sin(3*x)   2*(5 + 3*cos(3*x))                    \   2*(5*x + sin(3*x))|
x              *||-------------- + (5 + 3*cos(3*x))*log(x)|  - ----------- - 27*cos(3*x)*log(x) - ------------------ - 3*|-------------- + (5 + 3*cos(3*x))*log(x)|*|-------------- - ------------------ + 9*log(x)*sin(3*x)| + ------------------|
                |\      x                                 /         x                                      2             \      x                                 / |       2                 x                             |            3        |
                \                                                                                         x                                                         \      x                                                /           x         /

$$x^{5 x + \sin{\left(3 x \right)}} \left(\left(\left(3 \cos{\left(3 x \right)} + 5\right) \log{\left(x \right)} + \frac{5 x + \sin{\left(3 x \right)}}{x}\right)^{3} - 3 \left(\left(3 \cos{\left(3 x \right)} + 5\right) \log{\left(x \right)} + \frac{5 x + \sin{\left(3 x \right)}}{x}\right) \left(9 \log{\left(x \right)} \sin{\left(3 x \right)} - \frac{2 \left(3 \cos{\left(3 x \right)} + 5\right)}{x} + \frac{5 x + \sin{\left(3 x \right)}}{x^{2}}\right) - 27 \log{\left(x \right)} \cos{\left(3 x \right)} - \frac{27 \sin{\left(3 x \right)}}{x} - \frac{3 \left(3 \cos{\left(3 x \right)} + 5\right)}{x^{2}} + \frac{2 \left(5 x + \sin{\left(3 x \right)}\right)}{x^{3}}\right)$$

Simplificar

Gráfico

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Derivada de x^(sin(3x)+5x)

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