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tan(x)^cot(x)
Derivada de la función/ cot(x)/ tan(x)/ tan(x)^cot(x)

Derivada de tan(x)^cot(x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

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

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
             /                             /       2   \       \
   cot(x)    |/        2   \               \1 + tan (x)/*cot(x)|
tan      (x)*|\-1 - cot (x)/*log(tan(x)) + --------------------|
             \                                    tan(x)       /
((tan⁡2(x)+1)cot⁡(x)tan⁡(x)+(−cot⁡2(x)−1)log⁡(tan⁡(x)))tan⁡cot⁡(x)(x)\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\tan{\left(x \right)}} + \left(- \cot^{2}{\left(x \right)} - 1\right) \log{\left(\tan{\left(x \right)} \right)}\right) \tan^{\cot{\left(x \right)}}{\left(x \right)}
Simplificar
Segunda derivada [src] 
             /                                                    2                                         2                                                                            \
             |/                              /       2   \       \                             /       2   \             /       2   \ /       2   \                                     |
   cot(x)    ||  /       2   \               \1 + tan (x)/*cot(x)|      /       2   \          \1 + tan (x)/ *cot(x)   2*\1 + cot (x)/*\1 + tan (x)/     /       2   \                   |
tan      (x)*||- \1 + cot (x)/*log(tan(x)) + --------------------|  + 2*\1 + tan (x)/*cot(x) - --------------------- - ----------------------------- + 2*\1 + cot (x)/*cot(x)*log(tan(x))|
             |\                                     tan(x)       /                                       2                         tan(x)                                                |
             \                                                                                        tan (x)                                                                            /
(((tan⁡2(x)+1)cot⁡(x)tan⁡(x)−(cot⁡2(x)+1)log⁡(tan⁡(x)))2−(tan⁡2(x)+1)2cot⁡(x)tan⁡2(x)−2(tan⁡2(x)+1)(cot⁡2(x)+1)tan⁡(x)+2(tan⁡2(x)+1)cot⁡(x)+2(cot⁡2(x)+1)log⁡(tan⁡(x))cot⁡(x))tan⁡cot⁡(x)(x)\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\tan{\left(x \right)}} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)}\right)^{2} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cot{\left(x \right)}}{\tan^{2}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)} \cot{\left(x \right)}\right) \tan^{\cot{\left(x \right)}}{\left(x \right)}
Simplificar
Tercera derivada [src] 
             /                                                    3                                                                                          /                                        2                                                                            \                                                 2                                                               3                         2                                                                                     \
             |/                              /       2   \       \                                      /                              /       2   \       \ |                           /       2   \                                                  /       2   \ /       2   \|                  2                 /       2   \                                                   /       2   \             /       2   \  /       2   \                                     /       2   \ /       2   \       |
   cot(x)    ||  /       2   \               \1 + tan (x)/*cot(x)|      /       2   \ /       2   \     |  /       2   \               \1 + tan (x)/*cot(x)| |    /       2   \          \1 + tan (x)/ *cot(x)     /       2   \                      2*\1 + cot (x)/*\1 + tan (x)/|     /       2   \                4*\1 + tan (x)/ *cot(x)        2    /       2   \               2*\1 + tan (x)/ *cot(x)   3*\1 + tan (x)/ *\1 + cot (x)/     /       2   \                 6*\1 + cot (x)/*\1 + tan (x)/*cot(x)|
tan      (x)*||- \1 + cot (x)/*log(tan(x)) + --------------------|  - 6*\1 + cot (x)/*\1 + tan (x)/ - 3*|- \1 + cot (x)/*log(tan(x)) + --------------------|*|- 2*\1 + tan (x)/*cot(x) + --------------------- - 2*\1 + cot (x)/*cot(x)*log(tan(x)) + -----------------------------| - 2*\1 + cot (x)/ *log(tan(x)) - ----------------------- - 4*cot (x)*\1 + cot (x)/*log(tan(x)) + ----------------------- + ------------------------------ + 4*\1 + tan (x)/*cot(x)*tan(x) + ------------------------------------|
             |\                                     tan(x)       /                                      \                                     tan(x)       / |                                     2                                                              tan(x)           |                                           tan(x)                                                            3                            2                                                                 tan(x)               |
             \                                                                                                                                               \                                  tan (x)                                                                            /                                                                                                          tan (x)                      tan (x)                                                                                   /
(((tan⁡2(x)+1)cot⁡(x)tan⁡(x)−(cot⁡2(x)+1)log⁡(tan⁡(x)))3−3((tan⁡2(x)+1)cot⁡(x)tan⁡(x)−(cot⁡2(x)+1)log⁡(tan⁡(x)))((tan⁡2(x)+1)2cot⁡(x)tan⁡2(x)+2(tan⁡2(x)+1)(cot⁡2(x)+1)tan⁡(x)−2(tan⁡2(x)+1)cot⁡(x)−2(cot⁡2(x)+1)log⁡(tan⁡(x))cot⁡(x))+2(tan⁡2(x)+1)3cot⁡(x)tan⁡3(x)+3(tan⁡2(x)+1)2(cot⁡2(x)+1)tan⁡2(x)−4(tan⁡2(x)+1)2cot⁡(x)tan⁡(x)−6(tan⁡2(x)+1)(cot⁡2(x)+1)+6(tan⁡2(x)+1)(cot⁡2(x)+1)cot⁡(x)tan⁡(x)+4(tan⁡2(x)+1)tan⁡(x)cot⁡(x)−2(cot⁡2(x)+1)2log⁡(tan⁡(x))−4(cot⁡2(x)+1)log⁡(tan⁡(x))cot⁡2(x))tan⁡cot⁡(x)(x)\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\tan{\left(x \right)}} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)}\right)^{3} - 3 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\tan{\left(x \right)}} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cot{\left(x \right)}}{\tan^{2}{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)} \cot{\left(x \right)}\right) + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \cot{\left(x \right)}}{\tan^{3}{\left(x \right)}} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cot{\left(x \right)}}{\tan{\left(x \right)}} - 6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\tan{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \cot{\left(x \right)} - 2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\tan{\left(x \right)} \right)} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)} \cot^{2}{\left(x \right)}\right) \tan^{\cot{\left(x \right)}}{\left(x \right)}
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Gráfico
Derivada de tan(x)^cot(x)
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