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(tgx)^sin2x
Derivada de la función/ sin2x/ (tgx)/ (tgx)^sin2x

Derivada de (tgx)^sin2x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   sin(2*x)   
tan        (x)
tan⁡sin⁡(2x)(x)\tan^{\sin{\left(2 x \right)}}{\left(x \right)} 
tan(x)^sin(2*x)
Solución detallada

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

    Perola derivada

    (log⁡(sin⁡(2x))+1)sin⁡sin⁡(2x)(2x)\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \right)}

Respuesta:

(log⁡(sin⁡(2x))+1)sin⁡sin⁡(2x)(2x)\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \right)}

Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
               /                         /       2   \         \
   sin(2*x)    |                         \1 + tan (x)/*sin(2*x)|
tan        (x)*|2*cos(2*x)*log(tan(x)) + ----------------------|
               \                                 tan(x)        /
((tan⁡2(x)+1)sin⁡(2x)tan⁡(x)+2log⁡(tan⁡(x))cos⁡(2x))tan⁡sin⁡(2x)(x)\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}\right) \tan^{\sin{\left(2 x \right)}}{\left(x \right)}
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Segunda derivada [src] 
               /                                                 2                                                                    2                                    \
               |/                         /       2   \         \                                                        /       2   \               /       2   \         |
   sin(2*x)    ||                         \1 + tan (x)/*sin(2*x)|                               /       2   \            \1 + tan (x)/ *sin(2*x)   4*\1 + tan (x)/*cos(2*x)|
tan        (x)*||2*cos(2*x)*log(tan(x)) + ----------------------|  - 4*log(tan(x))*sin(2*x) + 2*\1 + tan (x)/*sin(2*x) - ----------------------- + ------------------------|
               |\                                 tan(x)        /                                                                   2                       tan(x)         |
               \                                                                                                                 tan (x)                                   /
(((tan⁡2(x)+1)sin⁡(2x)tan⁡(x)+2log⁡(tan⁡(x))cos⁡(2x))2−(tan⁡2(x)+1)2sin⁡(2x)tan⁡2(x)+2(tan⁡2(x)+1)sin⁡(2x)+4(tan⁡2(x)+1)cos⁡(2x)tan⁡(x)−4log⁡(tan⁡(x))sin⁡(2x))tan⁡sin⁡(2x)(x)\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}\right)^{2} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(2 x \right)}}{\tan{\left(x \right)}} - 4 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(2 x \right)}\right) \tan^{\sin{\left(2 x \right)}}{\left(x \right)}
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Tercera derivada [src] 
               /                                                 3                                                                                /                                                                   2                                    \                                                                          2                           2                           3                                           \
               |/                         /       2   \         \                               /                         /       2   \         \ |                                                      /       2   \               /       2   \         |                                  /       2   \              /       2   \               /       2   \               /       2   \                                            |
   sin(2*x)    ||                         \1 + tan (x)/*sin(2*x)|                               |                         \1 + tan (x)/*sin(2*x)| |    /       2   \                                     \1 + tan (x)/ *sin(2*x)   4*\1 + tan (x)/*cos(2*x)|      /       2   \            12*\1 + tan (x)/*sin(2*x)   6*\1 + tan (x)/ *cos(2*x)   4*\1 + tan (x)/ *sin(2*x)   2*\1 + tan (x)/ *sin(2*x)     /       2   \                |
tan        (x)*||2*cos(2*x)*log(tan(x)) + ----------------------|  - 8*cos(2*x)*log(tan(x)) - 3*|2*cos(2*x)*log(tan(x)) + ----------------------|*|- 2*\1 + tan (x)/*sin(2*x) + 4*log(tan(x))*sin(2*x) + ----------------------- - ------------------------| + 12*\1 + tan (x)/*cos(2*x) - ------------------------- - ------------------------- - ------------------------- + ------------------------- + 4*\1 + tan (x)/*sin(2*x)*tan(x)|
               |\                                 tan(x)        /                               \                                 tan(x)        / |                                                                 2                       tan(x)         |                                         tan(x)                        2                         tan(x)                        3                                              |
               \                                                                                                                                  \                                                              tan (x)                                   /                                                                    tan (x)                                                 tan (x)                                           /
(((tan⁡2(x)+1)sin⁡(2x)tan⁡(x)+2log⁡(tan⁡(x))cos⁡(2x))3−3((tan⁡2(x)+1)sin⁡(2x)tan⁡(x)+2log⁡(tan⁡(x))cos⁡(2x))((tan⁡2(x)+1)2sin⁡(2x)tan⁡2(x)−2(tan⁡2(x)+1)sin⁡(2x)−4(tan⁡2(x)+1)cos⁡(2x)tan⁡(x)+4log⁡(tan⁡(x))sin⁡(2x))+2(tan⁡2(x)+1)3sin⁡(2x)tan⁡3(x)−4(tan⁡2(x)+1)2sin⁡(2x)tan⁡(x)−6(tan⁡2(x)+1)2cos⁡(2x)tan⁡2(x)+4(tan⁡2(x)+1)sin⁡(2x)tan⁡(x)−12(tan⁡2(x)+1)sin⁡(2x)tan⁡(x)+12(tan⁡2(x)+1)cos⁡(2x)−8log⁡(tan⁡(x))cos⁡(2x))tan⁡sin⁡(2x)(x)\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}\right)^{3} - 3 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\tan^{2}{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(2 x \right)}}{\tan{\left(x \right)}} + 4 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(2 x \right)}\right) + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \sin{\left(2 x \right)}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\tan{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(2 x \right)}}{\tan^{2}{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)} \tan{\left(x \right)} - \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(x \right)}} + 12 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(2 x \right)} - 8 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}\right) \tan^{\sin{\left(2 x \right)}}{\left(x \right)}
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Gráfico
Derivada de (tgx)^sin2x
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