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lnx^sinx
Derivada de la función/ x^sin/ lnx^sinx

Derivada de lnx^sinx

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   sin(x)   
log      (x)
$$\log{\left(x \right)}^{\sin{\left(x \right)}}$$ 
log(x)^sin(x)
Solución detallada

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

    Perola derivada

Respuesta:

Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   sin(x)    /                      sin(x) \
log      (x)*|cos(x)*log(log(x)) + --------|
             \                     x*log(x)/
$$\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}$$
Simplificar
Segunda derivada [src] 
             /                               2                                                         \
   sin(x)    |/                      sin(x) \                           sin(x)      sin(x)     2*cos(x)|
log      (x)*||cos(x)*log(log(x)) + --------|  - log(log(x))*sin(x) - --------- - ---------- + --------|
             |\                     x*log(x)/                          2           2    2      x*log(x)|
             \                                                        x *log(x)   x *log (x)           /
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right)^{2} - \log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x \log{\left(x \right)}} - \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}$$
Simplificar
Tercera derivada [src] 
             /                               3                                                                                                                                                                                            \
   sin(x)    |/                      sin(x) \                           /                      sin(x) \ /                       sin(x)      sin(x)     2*cos(x)\   3*sin(x)    3*cos(x)    3*cos(x)     2*sin(x)    2*sin(x)     3*sin(x) |
log      (x)*||cos(x)*log(log(x)) + --------|  - cos(x)*log(log(x)) - 3*|cos(x)*log(log(x)) + --------|*|log(log(x))*sin(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)/
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right)^{3} - 3 \left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x \log{\left(x \right)}} + \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}} + \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) - \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x \log{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x^{2} \log{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \sin{\left(x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}$$
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Gráfico
Derivada de lnx^sinx
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