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Derivada de x^-4/5
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Expresiones idénticas
y=((3x^ dos)- uno)^lnsinx
y es igual a ((3x al cuadrado ) menos 1) en el grado ln seno de x
y es igual a ((3x en el grado dos) menos uno) en el grado ln seno de x
y=((3x2)-1)lnsinx
y=3x2-1lnsinx
y=((3x²)-1)^lnsinx
y=((3x en el grado 2)-1) en el grado lnsinx
y=3x^2-1^lnsinx
Expresiones semejantes
y=((3x^2)+1)^lnsinx

Derivada de la función/ lnsinx/ y=((3x^2)-1)^lnsinx

Derivada de y=((3x^2)-1)^lnsinx

Solución

Ha introducido [src]

          log(sin(x))
/   2    \           
\3*x  - 1/

\left(3 x^{2} - 1\right)^{\log{\left(\sin{\left(x \right)} \right)}}

(3*x^2 - 1)^log(sin(x))

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

          log(sin(x)) /          /   2    \                  \
/   2    \            |cos(x)*log\3*x  - 1/   6*x*log(sin(x))|
\3*x  - 1/           *|-------------------- + ---------------|
                      |       sin(x)                 2       |
                      \                           3*x  - 1   /

\left(3 x^{2} - 1\right)^{\log{\left(\sin{\left(x \right)} \right)}} \left(\frac{6 x \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1} + \frac{\log{\left(3 x^{2} - 1 \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)

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Segunda derivada [src]

                       /                                         2                                                                                                   \
           log(sin(x)) |/          /        2\                  \                                        2       /        2\       2                                 |
/        2\            ||cos(x)*log\-1 + 3*x /   6*x*log(sin(x))|       /        2\   6*log(sin(x))   cos (x)*log\-1 + 3*x /   36*x *log(sin(x))      12*x*cos(x)    |
\-1 + 3*x /           *||--------------------- + ---------------|  - log\-1 + 3*x / + ------------- - ---------------------- - ----------------- + ------------------|
                       ||        sin(x)                     2   |                               2               2                            2     /        2\       |
                       |\                           -1 + 3*x    /                       -1 + 3*x             sin (x)              /        2\      \-1 + 3*x /*sin(x)|
                       \                                                                                                          \-1 + 3*x /                        /

\left(3 x^{2} - 1\right)^{\log{\left(\sin{\left(x \right)} \right)}} \left(- \frac{36 x^{2} \log{\left(\sin{\left(x \right)} \right)}}{\left(3 x^{2} - 1\right)^{2}} + \frac{12 x \cos{\left(x \right)}}{\left(3 x^{2} - 1\right) \sin{\left(x \right)}} + \left(\frac{6 x \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1} + \frac{\log{\left(3 x^{2} - 1 \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} - \log{\left(3 x^{2} - 1 \right)} - \frac{\log{\left(3 x^{2} - 1 \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{6 \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1}\right)

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Tercera derivada [src]

                       /                                         3                                                                                                                                                                                                                                                                                                                              \
           log(sin(x)) |/          /        2\                  \                  /          /        2\                  \ /                     2       /        2\       2                                                  \                            3       /        2\               /        2\                             3                       2                         2      |
/        2\            ||cos(x)*log\-1 + 3*x /   6*x*log(sin(x))|       18*x       |cos(x)*log\-1 + 3*x /   6*x*log(sin(x))| |  6*log(sin(x))   cos (x)*log\-1 + 3*x /   36*x *log(sin(x))      12*x*cos(x)          /        2\|   108*x*log(sin(x))   2*cos (x)*log\-1 + 3*x /   2*cos(x)*log\-1 + 3*x /       18*cos(x)        432*x *log(sin(x))      108*x *cos(x)          18*x*cos (x)   |
\-1 + 3*x /           *||--------------------- + ---------------|  - --------- - 3*|--------------------- + ---------------|*|- ------------- + ---------------------- + ----------------- - ------------------ + log\-1 + 3*x /| - ----------------- + ------------------------ + ----------------------- + ------------------ + ------------------ - ------------------- - -------------------|
                       ||        sin(x)                     2   |            2     |        sin(x)                     2   | |            2               2                            2     /        2\                        |                 2                3                        sin(x)           /        2\                        3                 2          /        2\    2   |
                       |\                           -1 + 3*x    /    -1 + 3*x      \                           -1 + 3*x    / |    -1 + 3*x             sin (x)              /        2\      \-1 + 3*x /*sin(x)                 |      /        2\              sin (x)                                      \-1 + 3*x /*sin(x)      /        2\       /        2\           \-1 + 3*x /*sin (x)|
                       \                                                                                                     \                                              \-1 + 3*x /                                         /      \-1 + 3*x /                                                                                   \-1 + 3*x /       \-1 + 3*x / *sin(x)                      /

\left(3 x^{2} - 1\right)^{\log{\left(\sin{\left(x \right)} \right)}} \left(\frac{432 x^{3} \log{\left(\sin{\left(x \right)} \right)}}{\left(3 x^{2} - 1\right)^{3}} - \frac{108 x^{2} \cos{\left(x \right)}}{\left(3 x^{2} - 1\right)^{2} \sin{\left(x \right)}} - \frac{18 x}{3 x^{2} - 1} - \frac{18 x \cos^{2}{\left(x \right)}}{\left(3 x^{2} - 1\right) \sin^{2}{\left(x \right)}} - \frac{108 x \log{\left(\sin{\left(x \right)} \right)}}{\left(3 x^{2} - 1\right)^{2}} + \left(\frac{6 x \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1} + \frac{\log{\left(3 x^{2} - 1 \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} - 3 \left(\frac{6 x \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1} + \frac{\log{\left(3 x^{2} - 1 \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\frac{36 x^{2} \log{\left(\sin{\left(x \right)} \right)}}{\left(3 x^{2} - 1\right)^{2}} - \frac{12 x \cos{\left(x \right)}}{\left(3 x^{2} - 1\right) \sin{\left(x \right)}} + \log{\left(3 x^{2} - 1 \right)} + \frac{\log{\left(3 x^{2} - 1 \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{6 \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1}\right) + \frac{2 \log{\left(3 x^{2} - 1 \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \log{\left(3 x^{2} - 1 \right)} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{18 \cos{\left(x \right)}}{\left(3 x^{2} - 1\right) \sin{\left(x \right)}}\right)

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Gráfico

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Expresiones idénticas

Expresiones semejantes

Derivada de y=((3x^2)-1)^lnsinx

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Solución