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x^(sin(3*x)/2)

Derivada de x^(sin(3*x)/2)

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

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Solución

Ha introducido [src]
 sin(3*x)
 --------
    2    
x        
$$x^{\frac{\sin{\left(3 x \right)}}{2}}$$
x^(sin(3*x)/2)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
 sin(3*x)                               
 --------                               
    2     /sin(3*x)   3*cos(3*x)*log(x)\
x        *|-------- + -----------------|
          \  2*x              2        /
$$x^{\frac{\sin{\left(3 x \right)}}{2}} \left(\frac{3 \log{\left(x \right)} \cos{\left(3 x \right)}}{2} + \frac{\sin{\left(3 x \right)}}{2 x}\right)$$
Segunda derivada [src]
          /                              2                                            \
 sin(3*x) |/sin(3*x)                    \                                             |
 -------- ||-------- + 3*cos(3*x)*log(x)|                                             |
    2     |\   x                        /    3*cos(3*x)   9*log(x)*sin(3*x)   sin(3*x)|
x        *|------------------------------- + ---------- - ----------------- - --------|
          |               4                      x                2                2  |
          \                                                                     2*x   /
$$x^{\frac{\sin{\left(3 x \right)}}{2}} \left(\frac{\left(3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}\right)^{2}}{4} - \frac{9 \log{\left(x \right)} \sin{\left(3 x \right)}}{2} + \frac{3 \cos{\left(3 x \right)}}{x} - \frac{\sin{\left(3 x \right)}}{2 x^{2}}\right)$$
Tercera derivada [src]
          /                              3                                                                /sin(3*x)                    \ /sin(3*x)   6*cos(3*x)                    \\
 sin(3*x) |/sin(3*x)                    \                                                               3*|-------- + 3*cos(3*x)*log(x)|*|-------- - ---------- + 9*log(x)*sin(3*x)||
 -------- ||-------- + 3*cos(3*x)*log(x)|                                                                 \   x                        / |    2          x                         ||
    2     |\   x                        /    sin(3*x)   27*sin(3*x)   27*cos(3*x)*log(x)   9*cos(3*x)                                    \   x                                     /|
x        *|------------------------------- + -------- - ----------- - ------------------ - ---------- - ----------------------------------------------------------------------------|
          |               8                      3          2*x               2                  2                                           4                                      |
          \                                     x                                             2*x                                                                                   /
$$x^{\frac{\sin{\left(3 x \right)}}{2}} \left(\frac{\left(3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}\right)^{3}}{8} - \frac{3 \left(3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}\right) \left(9 \log{\left(x \right)} \sin{\left(3 x \right)} - \frac{6 \cos{\left(3 x \right)}}{x} + \frac{\sin{\left(3 x \right)}}{x^{2}}\right)}{4} - \frac{27 \log{\left(x \right)} \cos{\left(3 x \right)}}{2} - \frac{27 \sin{\left(3 x \right)}}{2 x} - \frac{9 \cos{\left(3 x \right)}}{2 x^{2}} + \frac{\sin{\left(3 x \right)}}{x^{3}}\right)$$
Gráfico
Derivada de x^(sin(3*x)/2)