Derivada de y=(lnx)^sin(5x)

Ha introducido [src]

   sin(5*x)   
log        (x)

\log{\left(x \right)}^{\sin{\left(5 x \right)}}

log(x)^sin(5*x)

Solución detallada

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Perola derivada

$\left(\log{\left(\sin{\left(5 x \right)} \right)} + 1\right) \sin^{\sin{\left(5 x \right)}}{\left(5 x \right)}$

Respuesta:

$\left(\log{\left(\sin{\left(5 x \right)} \right)} + 1\right) \sin^{\sin{\left(5 x \right)}}{\left(5 x \right)}$

Gráfica

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Primera derivada [src]

   sin(5*x)    /                         sin(5*x)\
log        (x)*|5*cos(5*x)*log(log(x)) + --------|
               \                         x*log(x)/

\left(5 \log{\left(\log{\left(x \right)} \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\sin{\left(5 x \right)}}

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Segunda derivada [src]

               /                                   2                                                                 \
   sin(5*x)    |/                         sin(5*x)\                               sin(5*x)    sin(5*x)    10*cos(5*x)|
log        (x)*||5*cos(5*x)*log(log(x)) + --------|  - 25*log(log(x))*sin(5*x) - --------- - ---------- + -----------|
               |\                         x*log(x)/                               2           2    2        x*log(x) |
               \                                                                 x *log(x)   x *log (x)              /

\left(\left(5 \log{\left(\log{\left(x \right)} \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x \log{\left(x \right)}}\right)^{2} - 25 \log{\left(\log{\left(x \right)} \right)} \sin{\left(5 x \right)} + \frac{10 \cos{\left(5 x \right)}}{x \log{\left(x \right)}} - \frac{\sin{\left(5 x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\sin{\left(5 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{\sin{\left(5 x \right)}}

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Tercera derivada [src]

               /                                   3                                                                                                                                                                                                                     \
   sin(5*x)    |/                         sin(5*x)\                                 /                         sin(5*x)\ /                           sin(5*x)    sin(5*x)    10*cos(5*x)\   75*sin(5*x)   15*cos(5*x)   15*cos(5*x)   2*sin(5*x)   2*sin(5*x)   3*sin(5*x)|
log        (x)*||5*cos(5*x)*log(log(x)) + --------|  - 125*cos(5*x)*log(log(x)) - 3*|5*cos(5*x)*log(log(x)) + --------|*|25*log(log(x))*sin(5*x) + --------- + ---------- - -----------| - ----------- - ----------- - ----------- + ---------- + ---------- + ----------|
               |\                         x*log(x)/                                 \                         x*log(x)/ |                           2           2    2        x*log(x) |     x*log(x)      2             2    2       3            3    3       3    2   |
               \                                                                                                        \                          x *log(x)   x *log (x)              /                  x *log(x)     x *log (x)   x *log(x)    x *log (x)   x *log (x)/

\left(\left(5 \log{\left(\log{\left(x \right)} \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x \log{\left(x \right)}}\right)^{3} - 3 \left(5 \log{\left(\log{\left(x \right)} \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x \log{\left(x \right)}}\right) \left(25 \log{\left(\log{\left(x \right)} \right)} \sin{\left(5 x \right)} - \frac{10 \cos{\left(5 x \right)}}{x \log{\left(x \right)}} + \frac{\sin{\left(5 x \right)}}{x^{2} \log{\left(x \right)}} + \frac{\sin{\left(5 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) - 125 \log{\left(\log{\left(x \right)} \right)} \cos{\left(5 x \right)} - \frac{75 \sin{\left(5 x \right)}}{x \log{\left(x \right)}} - \frac{15 \cos{\left(5 x \right)}}{x^{2} \log{\left(x \right)}} - \frac{15 \cos{\left(5 x \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \sin{\left(5 x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \sin{\left(5 x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \sin{\left(5 x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{\sin{\left(5 x \right)}}

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Gráfico

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Derivada de y=(lnx)^sin(5x)

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