Derivada de x^(sin(5-2x))

Ha introducido [src]

 sin(5 - 2*x)
x

$$x^{\sin{\left(5 - 2 x \right)}}$$

x^sin(5 - 2*x)

Solución detallada

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

Perola derivada

$\left(\log{\left(\sin{\left(5 - 2 x \right)} \right)} + 1\right) \sin^{\sin{\left(5 - 2 x \right)}}{\left(5 - 2 x \right)}$
Simplificamos:

$\left(- \sin{\left(2 x - 5 \right)}\right)^{- \sin{\left(2 x - 5 \right)}} \left(\log{\left(- \sin{\left(2 x - 5 \right)} \right)} + 1\right)$

Respuesta:

$\left(- \sin{\left(2 x - 5 \right)}\right)^{- \sin{\left(2 x - 5 \right)}} \left(\log{\left(- \sin{\left(2 x - 5 \right)} \right)} + 1\right)$

Gráfica

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Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

                /                                        2                                                           \
 -sin(-5 + 2*x) |/sin(-5 + 2*x)                         \    sin(-5 + 2*x)   4*cos(-5 + 2*x)                         |
x              *||------------- + 2*cos(-5 + 2*x)*log(x)|  + ------------- - --------------- + 4*log(x)*sin(-5 + 2*x)|
                |\      x                               /           2               x                                |
                \                                                  x                                                 /

$$x^{- \sin{\left(2 x - 5 \right)}} \left(\left(2 \log{\left(x \right)} \cos{\left(2 x - 5 \right)} + \frac{\sin{\left(2 x - 5 \right)}}{x}\right)^{2} + 4 \log{\left(x \right)} \sin{\left(2 x - 5 \right)} - \frac{4 \cos{\left(2 x - 5 \right)}}{x} + \frac{\sin{\left(2 x - 5 \right)}}{x^{2}}\right)$$

Simplificar

Tercera derivada [src]

                /                                          3                                                                                                                                                                                        \
 -sin(-5 + 2*x) |  /sin(-5 + 2*x)                         \      /sin(-5 + 2*x)                         \ /sin(-5 + 2*x)   4*cos(-5 + 2*x)                         \   2*sin(-5 + 2*x)   6*cos(-5 + 2*x)                            12*sin(-5 + 2*x)|
x              *|- |------------- + 2*cos(-5 + 2*x)*log(x)|  - 3*|------------- + 2*cos(-5 + 2*x)*log(x)|*|------------- - --------------- + 4*log(x)*sin(-5 + 2*x)| - --------------- + --------------- + 8*cos(-5 + 2*x)*log(x) + ----------------|
                |  \      x                               /      \      x                               / |       2               x                                |           3                 2                                         x        |
                \                                                                                         \      x                                                 /          x                 x                                                   /

$$x^{- \sin{\left(2 x - 5 \right)}} \left(- \left(2 \log{\left(x \right)} \cos{\left(2 x - 5 \right)} + \frac{\sin{\left(2 x - 5 \right)}}{x}\right)^{3} - 3 \left(2 \log{\left(x \right)} \cos{\left(2 x - 5 \right)} + \frac{\sin{\left(2 x - 5 \right)}}{x}\right) \left(4 \log{\left(x \right)} \sin{\left(2 x - 5 \right)} - \frac{4 \cos{\left(2 x - 5 \right)}}{x} + \frac{\sin{\left(2 x - 5 \right)}}{x^{2}}\right) + 8 \log{\left(x \right)} \cos{\left(2 x - 5 \right)} + \frac{12 \sin{\left(2 x - 5 \right)}}{x} + \frac{6 \cos{\left(2 x - 5 \right)}}{x^{2}} - \frac{2 \sin{\left(2 x - 5 \right)}}{x^{3}}\right)$$

Simplificar

Gráfico

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Derivada de x^(sin(5-2x))

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