Derivada de y=(lg(x))^(sin(x))

Ha introducido [src]

   sin(x)   
log      (x)

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

log(x)^sin(x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

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)/

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

Simplificar

Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Derivada de y=(lg(x))^(sin(x))

Gráfico:

Definida a trozos:

Solución