Derivada de y=(cos(3x))^arcsin(3x)

Ha introducido [src]

   asin(3*x)     
cos         (3*x)

\cos^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}

cos(3*x)^asin(3*x)

Solución detallada

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

Perola derivada

$\left(\log{\left(\operatorname{asin}{\left(3 x \right)} \right)} + 1\right) \operatorname{asin}^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}$

Respuesta:

$\left(\log{\left(\operatorname{asin}{\left(3 x \right)} \right)} + 1\right) \operatorname{asin}^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

   asin(3*x)      /3*log(cos(3*x))   3*asin(3*x)*sin(3*x)\
cos         (3*x)*|--------------- - --------------------|
                  |    __________          cos(3*x)      |
                  |   /        2                         |
                  \ \/  1 - 9*x                          /

\left(- \frac{3 \sin{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos{\left(3 x \right)}} + \frac{3 \log{\left(\cos{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right) \cos^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}

Simplificar

Segunda derivada [src]

                    /                                      2                  2                                                            \
     asin(3*x)      |/  log(cos(3*x))   asin(3*x)*sin(3*x)\                sin (3*x)*asin(3*x)         2*sin(3*x)         3*x*log(cos(3*x))|
9*cos         (3*x)*||- ------------- + ------------------|  - asin(3*x) - ------------------- - ---------------------- + -----------------|
                    ||     __________        cos(3*x)     |                        2                __________                        3/2  |
                    ||    /        2                      |                     cos (3*x)          /        2               /       2\     |
                    \\  \/  1 - 9*x                       /                                      \/  1 - 9*x  *cos(3*x)     \1 - 9*x /     /

9 \left(\frac{3 x \log{\left(\cos{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\sin{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \frac{\log{\left(\cos{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right)^{2} - \frac{\sin^{2}{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} - \operatorname{asin}{\left(3 x \right)} - \frac{2 \sin{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \cos{\left(3 x \right)}}\right) \cos^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}

Simplificar

Tercera derivada [src]

                     /                                        3                                                                            /   2                                                                        \              2                                          3                      2                                       \
      asin(3*x)      |  /  log(cos(3*x))   asin(3*x)*sin(3*x)\          3         log(cos(3*x))     /  log(cos(3*x))   asin(3*x)*sin(3*x)\ |sin (3*x)*asin(3*x)   3*x*log(cos(3*x))         2*sin(3*x)                  |         3*sin (3*x)         2*asin(3*x)*sin(3*x)   2*sin (3*x)*asin(3*x)   27*x *log(cos(3*x))        9*x*sin(3*x)     |
27*cos         (3*x)*|- |- ------------- + ------------------|  - ------------- + ------------- + 3*|- ------------- + ------------------|*|------------------- - ----------------- + ---------------------- + asin(3*x)| - ----------------------- - -------------------- - --------------------- + ------------------- - ----------------------|
                     |  |     __________        cos(3*x)     |       __________             3/2     |     __________        cos(3*x)     | |        2                         3/2        __________                     |      __________                   cos(3*x)                  3                           5/2                3/2         |
                     |  |    /        2                      |      /        2    /       2\        |    /        2                      | |     cos (3*x)          /       2\          /        2                      |     /        2     2                                     cos (3*x)            /       2\         /       2\            |
                     \  \  \/  1 - 9*x                       /    \/  1 - 9*x     \1 - 9*x /        \  \/  1 - 9*x                       / \                        \1 - 9*x /        \/  1 - 9*x  *cos(3*x)            /   \/  1 - 9*x  *cos (3*x)                                                     \1 - 9*x /         \1 - 9*x /   *cos(3*x)/

27 \left(\frac{27 x^{2} \log{\left(\cos{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} - \frac{9 x \sin{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \cos{\left(3 x \right)}} - \left(\frac{\sin{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \frac{\log{\left(\cos{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right)^{3} + 3 \left(\frac{\sin{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \frac{\log{\left(\cos{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right) \left(- \frac{3 x \log{\left(\cos{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{\sin^{2}{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} + \operatorname{asin}{\left(3 x \right)} + \frac{2 \sin{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \cos{\left(3 x \right)}}\right) - \frac{2 \sin^{3}{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos^{3}{\left(3 x \right)}} - \frac{2 \sin{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \frac{3 \sin^{2}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \cos^{2}{\left(3 x \right)}} - \frac{3}{\sqrt{1 - 9 x^{2}}} + \frac{\log{\left(\cos{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right) \cos^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}

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Gráfico

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Derivada de y=(cos(3x))^arcsin(3x)

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