Sr Examen

Derivada de x^(cos2x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

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

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
 cos(2*x) /cos(2*x)                    \
x        *|-------- - 2*log(x)*sin(2*x)|
          \   x                        /
$$x^{\cos{\left(2 x \right)}} \left(- 2 \log{\left(x \right)} \sin{\left(2 x \right)} + \frac{\cos{\left(2 x \right)}}{x}\right)$$
Segunda derivada [src]
          /                                2                                            \
 cos(2*x) |/  cos(2*x)                    \    cos(2*x)   4*sin(2*x)                    |
x        *||- -------- + 2*log(x)*sin(2*x)|  - -------- - ---------- - 4*cos(2*x)*log(x)|
          |\     x                        /        2          x                         |
          \                                       x                                     /
$$x^{\cos{\left(2 x \right)}} \left(\left(2 \log{\left(x \right)} \sin{\left(2 x \right)} - \frac{\cos{\left(2 x \right)}}{x}\right)^{2} - 4 \log{\left(x \right)} \cos{\left(2 x \right)} - \frac{4 \sin{\left(2 x \right)}}{x} - \frac{\cos{\left(2 x \right)}}{x^{2}}\right)$$
Tercera derivada [src]
          /                                  3                                                                                                                                             \
 cos(2*x) |  /  cos(2*x)                    \    12*cos(2*x)   2*cos(2*x)     /  cos(2*x)                    \ /cos(2*x)   4*sin(2*x)                    \   6*sin(2*x)                    |
x        *|- |- -------- + 2*log(x)*sin(2*x)|  - ----------- + ---------- + 3*|- -------- + 2*log(x)*sin(2*x)|*|-------- + ---------- + 4*cos(2*x)*log(x)| + ---------- + 8*log(x)*sin(2*x)|
          |  \     x                        /         x             3         \     x                        / |    2          x                         |        2                        |
          \                                                        x                                           \   x                                     /       x                         /
$$x^{\cos{\left(2 x \right)}} \left(- \left(2 \log{\left(x \right)} \sin{\left(2 x \right)} - \frac{\cos{\left(2 x \right)}}{x}\right)^{3} + 3 \left(2 \log{\left(x \right)} \sin{\left(2 x \right)} - \frac{\cos{\left(2 x \right)}}{x}\right) \left(4 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{4 \sin{\left(2 x \right)}}{x} + \frac{\cos{\left(2 x \right)}}{x^{2}}\right) + 8 \log{\left(x \right)} \sin{\left(2 x \right)} - \frac{12 \cos{\left(2 x \right)}}{x} + \frac{6 \sin{\left(2 x \right)}}{x^{2}} + \frac{2 \cos{\left(2 x \right)}}{x^{3}}\right)$$
Gráfico
Derivada de x^(cos2x)