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Derivada de y=(tan^2(x))^(sin4x)

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

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Solución

Ha introducido [src]
       sin(4*x)
   2           
tan (x)        
$$\left(\tan^{2}{\left(x \right)}\right)^{\sin{\left(4 x \right)}}$$
(tan(x)^2)^sin(4*x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Primera derivada [src]
                   /                          /         2   \         \
        2*sin(4*x) |              /   2   \   \2 + 2*tan (x)/*sin(4*x)|
|tan(x)|          *|4*cos(4*x)*log\tan (x)/ + ------------------------|
                   \                                   tan(x)         /
$$\left(\frac{\left(2 \tan^{2}{\left(x \right)} + 2\right) \sin{\left(4 x \right)}}{\tan{\left(x \right)}} + 4 \log{\left(\tan^{2}{\left(x \right)} \right)} \cos{\left(4 x \right)}\right) \left|{\tan{\left(x \right)}}\right|^{2 \sin{\left(4 x \right)}}$$
Segunda derivada [src]
                     /                                                                                                                                                                                            2                                    \
                     |                                                         /                          /       2   \         \ /                           /       2   \                      \   /       2   \               /       2   \         |
          2*sin(4*x) |       /   2   \              /       2   \              |              /   2   \   \1 + tan (x)/*sin(4*x)| |                           \1 + tan (x)/*sign(tan(x))*sin(4*x)|   \1 + tan (x)/ *sin(4*x)   8*\1 + tan (x)/*cos(4*x)|
2*|tan(x)|          *|- 8*log\tan (x)/*sin(4*x) + 2*\1 + tan (x)/*sin(4*x) + 2*|2*cos(4*x)*log\tan (x)/ + ----------------------|*|4*cos(4*x)*log(|tan(x)|) + -----------------------------------| - ----------------------- + ------------------------|
                     |                                                         \                                  tan(x)        / \                                         |tan(x)|             /              2                       tan(x)         |
                     \                                                                                                                                                                                       tan (x)                                   /
$$2 \left(2 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan^{2}{\left(x \right)} \right)} \cos{\left(4 x \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} \operatorname{sign}{\left(\tan{\left(x \right)} \right)}}{\left|{\tan{\left(x \right)}}\right|} + 4 \log{\left(\left|{\tan{\left(x \right)}}\right| \right)} \cos{\left(4 x \right)}\right) - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(4 x \right)}}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(4 x \right)}}{\tan{\left(x \right)}} - 8 \log{\left(\tan^{2}{\left(x \right)} \right)} \sin{\left(4 x \right)}\right) \left|{\tan{\left(x \right)}}\right|^{2 \sin{\left(4 x \right)}}$$
Tercera derivada [src]
                     /                                                   /                                          2                                         2                                                                                                                   \                                                                                                 /                                                                    2                                    \                                                                     2                                                                                               3                                                       2                           2                                           \
                     |/                          /       2   \         \ |                             /       2   \      2                      /       2   \                                  /       2   \                           /       2   \                             |                                /                           /       2   \                      \ |                                                       /       2   \               /       2   \         |     /                           /       2   \                      \  /                          /       2   \         \                               /       2   \                /       2   \              /       2   \               /       2   \                                            |
          2*sin(4*x) ||              /   2   \   \1 + tan (x)/*sin(4*x)| |                             \1 + tan (x)/ *sign (tan(x))*sin(4*x)   2*\1 + tan (x)/ *DiracDelta(tan(x))*sin(4*x)   8*\1 + tan (x)/*cos(4*x)*sign(tan(x))   2*\1 + tan (x)/*sign(tan(x))*sin(4*x)*tan(x)|                  /   2   \     |                           \1 + tan (x)/*sign(tan(x))*sin(4*x)| |    /       2   \                 /   2   \            \1 + tan (x)/ *sin(4*x)   8*\1 + tan (x)/*cos(4*x)|     |                           \1 + tan (x)/*sign(tan(x))*sin(4*x)|  |              /   2   \   \1 + tan (x)/*sin(4*x)|      /       2   \            \1 + tan (x)/ *sin(4*x)   24*\1 + tan (x)/*sin(4*x)   6*\1 + tan (x)/ *cos(4*x)   2*\1 + tan (x)/ *sin(4*x)     /       2   \                |
4*|tan(x)|          *||2*cos(4*x)*log\tan (x)/ + ----------------------|*|-16*log(|tan(x)|)*sin(4*x) - ------------------------------------- + -------------------------------------------- + ------------------------------------- + --------------------------------------------| - 16*cos(4*x)*log\tan (x)/ - 2*|4*cos(4*x)*log(|tan(x)|) + -----------------------------------|*|- 2*\1 + tan (x)/*sin(4*x) + 8*log\tan (x)/*sin(4*x) + ----------------------- - ------------------------| + 2*|4*cos(4*x)*log(|tan(x)|) + -----------------------------------| *|2*cos(4*x)*log\tan (x)/ + ----------------------| + 12*\1 + tan (x)/*cos(4*x) + ----------------------- - ------------------------- - ------------------------- - ------------------------- + 2*\1 + tan (x)/*sin(4*x)*tan(x)|
                     |\                                  tan(x)        / |                                               2                                       |tan(x)|                                    |tan(x)|                                   |tan(x)|                  |                                \                                         |tan(x)|             / |                                                                  2                       tan(x)         |     \                                         |tan(x)|             /  \                                  tan(x)        /                                          3                        tan(x)                        2                         tan(x)                                           |
                     \                                                   \                                            tan (x)                                                                                                                                                     /                                                                                                 \                                                               tan (x)                                   /                                                                                                                                                                tan (x)                                                tan (x)                                                                       /
$$4 \left(2 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan^{2}{\left(x \right)} \right)} \cos{\left(4 x \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} \operatorname{sign}{\left(\tan{\left(x \right)} \right)}}{\left|{\tan{\left(x \right)}}\right|} + 4 \log{\left(\left|{\tan{\left(x \right)}}\right| \right)} \cos{\left(4 x \right)}\right)^{2} + \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan^{2}{\left(x \right)} \right)} \cos{\left(4 x \right)}\right) \left(\frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(4 x \right)} \delta\left(\tan{\left(x \right)}\right)}{\left|{\tan{\left(x \right)}}\right|} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(4 x \right)} \operatorname{sign}^{2}{\left(\tan{\left(x \right)} \right)}}{\tan^{2}{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} \tan{\left(x \right)} \operatorname{sign}{\left(\tan{\left(x \right)} \right)}}{\left|{\tan{\left(x \right)}}\right|} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(4 x \right)} \operatorname{sign}{\left(\tan{\left(x \right)} \right)}}{\left|{\tan{\left(x \right)}}\right|} - 16 \log{\left(\left|{\tan{\left(x \right)}}\right| \right)} \sin{\left(4 x \right)}\right) - 2 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} \operatorname{sign}{\left(\tan{\left(x \right)} \right)}}{\left|{\tan{\left(x \right)}}\right|} + 4 \log{\left(\left|{\tan{\left(x \right)}}\right| \right)} \cos{\left(4 x \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(4 x \right)}}{\tan^{2}{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} - \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(4 x \right)}}{\tan{\left(x \right)}} + 8 \log{\left(\tan^{2}{\left(x \right)} \right)} \sin{\left(4 x \right)}\right) + \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{3} \sin{\left(4 x \right)}}{\tan^{3}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(4 x \right)}}{\tan{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(4 x \right)}}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} \tan{\left(x \right)} - \frac{24 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)}}{\tan{\left(x \right)}} + 12 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(4 x \right)} - 16 \log{\left(\tan^{2}{\left(x \right)} \right)} \cos{\left(4 x \right)}\right) \left|{\tan{\left(x \right)}}\right|^{2 \sin{\left(4 x \right)}}$$