Derivada de y=(sin3x)^(ln2x)

Ha introducido [src]

   log(2*x)     
sin        (3*x)

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

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

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

                 /                                     2                                     2                           \
   log(2*x)      |/log(sin(3*x))   3*cos(3*x)*log(2*x)\                 log(sin(3*x))   9*cos (3*x)*log(2*x)   6*cos(3*x)|
sin        (3*x)*||------------- + -------------------|  - 9*log(2*x) - ------------- - -------------------- + ----------|
                 |\      x               sin(3*x)     /                        2                2              x*sin(3*x)|
                 \                                                            x              sin (3*x)                   /

$$\left(\left(\frac{3 \log{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(3 x \right)}} + \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{x}\right)^{2} - 9 \log{\left(2 x \right)} - \frac{9 \log{\left(2 x \right)} \cos^{2}{\left(3 x \right)}}{\sin^{2}{\left(3 x \right)}} + \frac{6 \cos{\left(3 x \right)}}{x \sin{\left(3 x \right)}} - \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{x^{2}}\right) \sin^{\log{\left(2 x \right)}}{\left(3 x \right)}$$

Simplificar

3-я производная [src]

                 /                                     3                                                /                                               2              \                           2                            3                                     \
   log(2*x)      |/log(sin(3*x))   3*cos(3*x)*log(2*x)\    27     /log(sin(3*x))   3*cos(3*x)*log(2*x)\ |             log(sin(3*x))   6*cos(3*x)   9*cos (3*x)*log(2*x)|   2*log(sin(3*x))   27*cos (3*x)    9*cos(3*x)   54*cos (3*x)*log(2*x)   54*cos(3*x)*log(2*x)|
sin        (3*x)*||------------- + -------------------|  - -- - 3*|------------- + -------------------|*|9*log(2*x) + ------------- - ---------- + --------------------| + --------------- - ------------ - ----------- + --------------------- + --------------------|
                 |\      x               sin(3*x)     /    x      \      x               sin(3*x)     / |                    2        x*sin(3*x)           2           |           3              2          2                     3                    sin(3*x)      |
                 \                                                                                      \                   x                           sin (3*x)      /          x          x*sin (3*x)    x *sin(3*x)         sin (3*x)                             /

$$\left(\left(\frac{3 \log{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(3 x \right)}} + \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{3 \log{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(3 x \right)}} + \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{x}\right) \left(9 \log{\left(2 x \right)} + \frac{9 \log{\left(2 x \right)} \cos^{2}{\left(3 x \right)}}{\sin^{2}{\left(3 x \right)}} - \frac{6 \cos{\left(3 x \right)}}{x \sin{\left(3 x \right)}} + \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{x^{2}}\right) + \frac{54 \log{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(3 x \right)}} + \frac{54 \log{\left(2 x \right)} \cos^{3}{\left(3 x \right)}}{\sin^{3}{\left(3 x \right)}} - \frac{27}{x} - \frac{27 \cos^{2}{\left(3 x \right)}}{x \sin^{2}{\left(3 x \right)}} - \frac{9 \cos{\left(3 x \right)}}{x^{2} \sin{\left(3 x \right)}} + \frac{2 \log{\left(\sin{\left(3 x \right)} \right)}}{x^{3}}\right) \sin^{\log{\left(2 x \right)}}{\left(3 x \right)}$$

Simplificar

Tercera derivada [src]

                 /                                     3                                                /                                               2              \                           2                            3                                     \
   log(2*x)      |/log(sin(3*x))   3*cos(3*x)*log(2*x)\    27     /log(sin(3*x))   3*cos(3*x)*log(2*x)\ |             log(sin(3*x))   6*cos(3*x)   9*cos (3*x)*log(2*x)|   2*log(sin(3*x))   27*cos (3*x)    9*cos(3*x)   54*cos (3*x)*log(2*x)   54*cos(3*x)*log(2*x)|
sin        (3*x)*||------------- + -------------------|  - -- - 3*|------------- + -------------------|*|9*log(2*x) + ------------- - ---------- + --------------------| + --------------- - ------------ - ----------- + --------------------- + --------------------|
                 |\      x               sin(3*x)     /    x      \      x               sin(3*x)     / |                    2        x*sin(3*x)           2           |           3              2          2                     3                    sin(3*x)      |
                 \                                                                                      \                   x                           sin (3*x)      /          x          x*sin (3*x)    x *sin(3*x)         sin (3*x)                             /

$$\left(\left(\frac{3 \log{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(3 x \right)}} + \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{3 \log{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(3 x \right)}} + \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{x}\right) \left(9 \log{\left(2 x \right)} + \frac{9 \log{\left(2 x \right)} \cos^{2}{\left(3 x \right)}}{\sin^{2}{\left(3 x \right)}} - \frac{6 \cos{\left(3 x \right)}}{x \sin{\left(3 x \right)}} + \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{x^{2}}\right) + \frac{54 \log{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(3 x \right)}} + \frac{54 \log{\left(2 x \right)} \cos^{3}{\left(3 x \right)}}{\sin^{3}{\left(3 x \right)}} - \frac{27}{x} - \frac{27 \cos^{2}{\left(3 x \right)}}{x \sin^{2}{\left(3 x \right)}} - \frac{9 \cos{\left(3 x \right)}}{x^{2} \sin{\left(3 x \right)}} + \frac{2 \log{\left(\sin{\left(3 x \right)} \right)}}{x^{3}}\right) \sin^{\log{\left(2 x \right)}}{\left(3 x \right)}$$

Simplificar

Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Derivada de y=(sin3x)^(ln2x)

Gráfico:

Definida a trozos:

Solución