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y=(sin3x)^(ln2x)
Derivada de la función/ sin3x/ y=(sin3x)^(ln2x)

Derivada de y=(sin3x)^(ln2x)

Función f() - derivada -er orden en el punto
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Solución

Ha introducido [src] 
   log(2*x)     
sin        (3*x)
sin⁡log⁡(2x)(3x)\sin^{\log{\left(2 x \right)}}{\left(3 x \right)} 
sin(3*x)^log(2*x)
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-200200
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)     /
(3log⁡(2x)cos⁡(3x)sin⁡(3x)+log⁡(sin⁡(3x))x)sin⁡log⁡(2x)(3x)\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)}
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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)                   /
((3log⁡(2x)cos⁡(3x)sin⁡(3x)+log⁡(sin⁡(3x))x)2−9log⁡(2x)−9log⁡(2x)cos⁡2(3x)sin⁡2(3x)+6cos⁡(3x)xsin⁡(3x)−log⁡(sin⁡(3x))x2)sin⁡log⁡(2x)(3x)\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)                             /
((3log⁡(2x)cos⁡(3x)sin⁡(3x)+log⁡(sin⁡(3x))x)3−3(3log⁡(2x)cos⁡(3x)sin⁡(3x)+log⁡(sin⁡(3x))x)(9log⁡(2x)+9log⁡(2x)cos⁡2(3x)sin⁡2(3x)−6cos⁡(3x)xsin⁡(3x)+log⁡(sin⁡(3x))x2)+54log⁡(2x)cos⁡(3x)sin⁡(3x)+54log⁡(2x)cos⁡3(3x)sin⁡3(3x)−27x−27cos⁡2(3x)xsin⁡2(3x)−9cos⁡(3x)x2sin⁡(3x)+2log⁡(sin⁡(3x))x3)sin⁡log⁡(2x)(3x)\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)                             /
((3log⁡(2x)cos⁡(3x)sin⁡(3x)+log⁡(sin⁡(3x))x)3−3(3log⁡(2x)cos⁡(3x)sin⁡(3x)+log⁡(sin⁡(3x))x)(9log⁡(2x)+9log⁡(2x)cos⁡2(3x)sin⁡2(3x)−6cos⁡(3x)xsin⁡(3x)+log⁡(sin⁡(3x))x2)+54log⁡(2x)cos⁡(3x)sin⁡(3x)+54log⁡(2x)cos⁡3(3x)sin⁡3(3x)−27x−27cos⁡2(3x)xsin⁡2(3x)−9cos⁡(3x)x2sin⁡(3x)+2log⁡(sin⁡(3x))x3)sin⁡log⁡(2x)(3x)\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)}
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Gráfico
Derivada de y=(sin3x)^(ln2x)
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