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x^(sin(2(x+100)))

Derivada de x^(sin(2(x+100)))

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Ha introducido [src]
 sin(2*(x + 100))
x                
$$x^{\sin{\left(2 \left(x + 100\right) \right)}}$$
x^sin(2*(x + 100))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
 sin(2*(x + 100)) /sin(2*(x + 100))                            \
x                *|---------------- + 2*cos(2*(x + 100))*log(x)|
                  \       x                                    /
$$x^{\sin{\left(2 \left(x + 100\right) \right)}} \left(2 \log{\left(x \right)} \cos{\left(2 \left(x + 100\right) \right)} + \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x}\right)$$
Segunda derivada [src]
                  /                                              2                                                                    \
 sin(2*(100 + x)) |/sin(2*(100 + x))                            \    sin(2*(100 + x))                               4*cos(2*(100 + x))|
x                *||---------------- + 2*cos(2*(100 + x))*log(x)|  - ---------------- - 4*log(x)*sin(2*(100 + x)) + ------------------|
                  |\       x                                    /            2                                              x         |
                  \                                                         x                                                         /
$$x^{\sin{\left(2 \left(x + 100\right) \right)}} \left(\left(2 \log{\left(x \right)} \cos{\left(2 \left(x + 100\right) \right)} + \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x}\right)^{2} - 4 \log{\left(x \right)} \sin{\left(2 \left(x + 100\right) \right)} + \frac{4 \cos{\left(2 \left(x + 100\right) \right)}}{x} - \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x^{2}}\right)$$
Tercera derivada [src]
                  /                                              3                                                                                                                                                                                                                   \
 sin(2*(100 + x)) |/sin(2*(100 + x))                            \    12*sin(2*(100 + x))                               6*cos(2*(100 + x))     /sin(2*(100 + x))                            \ /sin(2*(100 + x))   4*cos(2*(100 + x))                            \   2*sin(2*(100 + x))|
x                *||---------------- + 2*cos(2*(100 + x))*log(x)|  - ------------------- - 8*cos(2*(100 + x))*log(x) - ------------------ - 3*|---------------- + 2*cos(2*(100 + x))*log(x)|*|---------------- - ------------------ + 4*log(x)*sin(2*(100 + x))| + ------------------|
                  |\       x                                    /             x                                                 2             \       x                                    / |        2                  x                                     |            3        |
                  \                                                                                                            x                                                             \       x                                                         /           x         /
$$x^{\sin{\left(2 \left(x + 100\right) \right)}} \left(\left(2 \log{\left(x \right)} \cos{\left(2 \left(x + 100\right) \right)} + \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x}\right)^{3} - 3 \left(2 \log{\left(x \right)} \cos{\left(2 \left(x + 100\right) \right)} + \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x}\right) \left(4 \log{\left(x \right)} \sin{\left(2 \left(x + 100\right) \right)} - \frac{4 \cos{\left(2 \left(x + 100\right) \right)}}{x} + \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x^{2}}\right) - 8 \log{\left(x \right)} \cos{\left(2 \left(x + 100\right) \right)} - \frac{12 \sin{\left(2 \left(x + 100\right) \right)}}{x} - \frac{6 \cos{\left(2 \left(x + 100\right) \right)}}{x^{2}} + \frac{2 \sin{\left(2 \left(x + 100\right) \right)}}{x^{3}}\right)$$
Gráfico
Derivada de x^(sin(2(x+100)))