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y=(tgx)^(4e)^x
Derivada de la función/ (tgx)/ y=(tgx)^(4e)^x

Derivada de y=(tgx)^(4e)^x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
        /     x\
        \(4*E) /
(tan(x))
tan⁡(4e)x(x)\tan^{\left(4 e\right)^{x}}{\left(x \right)} 
tan(x)^((4*E)^x)
Solución detallada

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

    Perola derivada

    (4e)x(4e)x(log⁡((4e)x)+1)\left(4 e\right)^{x \left(4 e\right)^{x}} \left(\log{\left(\left(4 e\right)^{x} \right)} + 1\right)

Respuesta:

(4e)x(4e)x(log⁡((4e)x)+1)\left(4 e\right)^{x \left(4 e\right)^{x}} \left(\log{\left(\left(4 e\right)^{x} \right)} + 1\right)

Gráfica
02468-8-6-4-2-101001e135
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        /     x\ /     x /       2   \                              \
        \(4*E) / |(4*E) *\1 + tan (x)/        x                     |
(tan(x))        *|-------------------- + (4*E) *log(4*E)*log(tan(x))|
                 \       tan(x)                                     /
((4e)x(tan⁡2(x)+1)tan⁡(x)+(4e)xlog⁡(4e)log⁡(tan⁡(x)))tan⁡(4e)x(x)\left(\frac{\left(4 e\right)^{x} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \left(4 e\right)^{x} \log{\left(4 e \right)} \log{\left(\tan{\left(x \right)} \right)}\right) \tan^{\left(4 e\right)^{x}}{\left(x \right)}
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Segunda derivada [src] 
                        /                                                           2                                        2                           \
               /     x\ |                       /       2                          \                            /       2   \      /       2   \         |
     x         \(4*E) / |         2           x |1 + tan (x)                       |       2                    \1 + tan (x)/    2*\1 + tan (x)/*log(4*E)|
(4*E) *(tan(x))        *|2 + 2*tan (x) + (4*E) *|----------- + log(4*E)*log(tan(x))|  + log (4*E)*log(tan(x)) - -------------- + ------------------------|
                        |                       \   tan(x)                         /                                  2                   tan(x)         |
                        \                                                                                          tan (x)                               /
(4e)x((4e)x(tan⁡2(x)+1tan⁡(x)+log⁡(4e)log⁡(tan⁡(x)))2−(tan⁡2(x)+1)2tan⁡2(x)+2(tan⁡2(x)+1)log⁡(4e)tan⁡(x)+log⁡(4e)2log⁡(tan⁡(x))+2tan⁡2(x)+2)tan⁡(4e)x(x)\left(4 e\right)^{x} \left(\left(4 e\right)^{x} \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \log{\left(4 e \right)} \log{\left(\tan{\left(x \right)} \right)}\right)^{2} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(4 e \right)}}{\tan{\left(x \right)}} + \log{\left(4 e \right)}^{2} \log{\left(\tan{\left(x \right)} \right)} + 2 \tan^{2}{\left(x \right)} + 2\right) \tan^{\left(4 e\right)^{x}}{\left(x \right)}
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Tercera derivada [src] 
                        /                                             3                                          2                  3                                                                      2                                                          /                                                     2                           \                            \
               /     x\ |         /       2                          \                              /       2   \      /       2   \                                                          /       2   \                      /       2                          \ |                                        /       2   \      /       2   \         |        2      /       2   \|
     x         \(4*E) / |     2*x |1 + tan (x)                       |       3                    4*\1 + tan (x)/    2*\1 + tan (x)/      /       2   \            /       2   \            3*\1 + tan (x)/ *log(4*E)          x |1 + tan (x)                       | |         2         2                    \1 + tan (x)/    2*\1 + tan (x)/*log(4*E)|   3*log (4*E)*\1 + tan (x)/|
(4*E) *(tan(x))        *|(4*E)   *|----------- + log(4*E)*log(tan(x))|  + log (4*E)*log(tan(x)) - ---------------- + ---------------- + 4*\1 + tan (x)/*tan(x) + 6*\1 + tan (x)/*log(4*E) - ------------------------- + 3*(4*E) *|----------- + log(4*E)*log(tan(x))|*|2 + 2*tan (x) + log (4*E)*log(tan(x)) - -------------- + ------------------------| + -------------------------|
                        |         \   tan(x)                         /                                 tan(x)               3                                                                           2                        \   tan(x)                         / |                                              2                   tan(x)         |             tan(x)         |
                        \                                                                                                tan (x)                                                                     tan (x)                                                          \                                           tan (x)                               /                            /
(4e)x((4e)2x(tan⁡2(x)+1tan⁡(x)+log⁡(4e)log⁡(tan⁡(x)))3+3(4e)x(tan⁡2(x)+1tan⁡(x)+log⁡(4e)log⁡(tan⁡(x)))(−(tan⁡2(x)+1)2tan⁡2(x)+2(tan⁡2(x)+1)log⁡(4e)tan⁡(x)+log⁡(4e)2log⁡(tan⁡(x))+2tan⁡2(x)+2)+2(tan⁡2(x)+1)3tan⁡3(x)−4(tan⁡2(x)+1)2tan⁡(x)−3(tan⁡2(x)+1)2log⁡(4e)tan⁡2(x)+4(tan⁡2(x)+1)tan⁡(x)+6(tan⁡2(x)+1)log⁡(4e)+3(tan⁡2(x)+1)log⁡(4e)2tan⁡(x)+log⁡(4e)3log⁡(tan⁡(x)))tan⁡(4e)x(x)\left(4 e\right)^{x} \left(\left(4 e\right)^{2 x} \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \log{\left(4 e \right)} \log{\left(\tan{\left(x \right)} \right)}\right)^{3} + 3 \left(4 e\right)^{x} \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \log{\left(4 e \right)} \log{\left(\tan{\left(x \right)} \right)}\right) \left(- \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(4 e \right)}}{\tan{\left(x \right)}} + \log{\left(4 e \right)}^{2} \log{\left(\tan{\left(x \right)} \right)} + 2 \tan^{2}{\left(x \right)} + 2\right) + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(4 e \right)}}{\tan^{2}{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 6 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(4 e \right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(4 e \right)}^{2}}{\tan{\left(x \right)}} + \log{\left(4 e \right)}^{3} \log{\left(\tan{\left(x \right)} \right)}\right) \tan^{\left(4 e\right)^{x}}{\left(x \right)}
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Gráfico
Derivada de y=(tgx)^(4e)^x
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