Derivada de x^sin(2x-3)

Ha introducido [src]

 sin(2*x - 3)
x

$$x^{\sin{\left(2 x - 3 \right)}}$$

x^sin(2*x - 3)

Solución detallada

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

Perola derivada

$\left(\log{\left(\sin{\left(2 x - 3 \right)} \right)} + 1\right) \sin^{\sin{\left(2 x - 3 \right)}}{\left(2 x - 3 \right)}$
Simplificamos:

$\left(\log{\left(\sin{\left(2 x - 3 \right)} \right)} + 1\right) \sin^{\sin{\left(2 x - 3 \right)}}{\left(2 x - 3 \right)}$

Respuesta:

$\left(\log{\left(\sin{\left(2 x - 3 \right)} \right)} + 1\right) \sin^{\sin{\left(2 x - 3 \right)}}{\left(2 x - 3 \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

               /                                        2                                                           \
 sin(-3 + 2*x) |/sin(-3 + 2*x)                         \    sin(-3 + 2*x)                            4*cos(-3 + 2*x)|
x             *||------------- + 2*cos(-3 + 2*x)*log(x)|  - ------------- - 4*log(x)*sin(-3 + 2*x) + ---------------|
               |\      x                               /           2                                        x       |
               \                                                  x                                                 /

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

Simplificar

Tercera derivada [src]

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

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

Simplificar

Gráfico

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Derivada de x^sin(2x-3)

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