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y=(x^4+1)^tgx
Derivada de la función/ x^4+1/ y=(x^4+1)^tgx

Derivada de y=(x^4+1)^tgx

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
        tan(x)
/ 4    \      
\x  + 1/
(x4+1)tan⁡(x)\left(x^{4} + 1\right)^{\tan{\left(x \right)}} 
(x^4 + 1)^tan(x)
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-101001e81
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        tan(x) /                               3       \
/ 4    \       |/       2   \    / 4    \   4*x *tan(x)|
\x  + 1/      *|\1 + tan (x)/*log\x  + 1/ + -----------|
               |                                4      |
               \                               x  + 1  /
(x4+1)tan⁡(x)(4x3tan⁡(x)x4+1+(tan⁡2(x)+1)log⁡(x4+1))\left(x^{4} + 1\right)^{\tan{\left(x \right)}} \left(\frac{4 x^{3} \tan{\left(x \right)}}{x^{4} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 1 \right)}\right)
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Segunda derivada [src] 
               /                                         2                                                                                        \
        tan(x) |/                               3       \        6                                                  3 /       2   \       2       |
/     4\       ||/       2   \    /     4\   4*x *tan(x)|    16*x *tan(x)     /       2   \    /     4\          8*x *\1 + tan (x)/   12*x *tan(x)|
\1 + x /      *||\1 + tan (x)/*log\1 + x / + -----------|  - ------------ + 2*\1 + tan (x)/*log\1 + x /*tan(x) + ------------------ + ------------|
               ||                                    4  |             2                                                     4                 4   |
               |\                               1 + x   /     /     4\                                                 1 + x             1 + x    |
               \                                              \1 + x /                                                                            /
(x4+1)tan⁡(x)(−16x6tan⁡(x)(x4+1)2+8x3(tan⁡2(x)+1)x4+1+12x2tan⁡(x)x4+1+(4x3tan⁡(x)x4+1+(tan⁡2(x)+1)log⁡(x4+1))2+2(tan⁡2(x)+1)log⁡(x4+1)tan⁡(x))\left(x^{4} + 1\right)^{\tan{\left(x \right)}} \left(- \frac{16 x^{6} \tan{\left(x \right)}}{\left(x^{4} + 1\right)^{2}} + \frac{8 x^{3} \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{4} + 1} + \frac{12 x^{2} \tan{\left(x \right)}}{x^{4} + 1} + \left(\frac{4 x^{3} \tan{\left(x \right)}}{x^{4} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 1 \right)}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 1 \right)} \tan{\left(x \right)}\right)
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Tercera derivada [src] 
               /                                         3                                                                                                                                                                                                                                                                                                                              \
        tan(x) |/                               3       \                   2                 /                               3       \ /                                      6             3 /       2   \      2       \        5              6 /       2   \                                                           2 /       2   \        9              3 /       2   \       |
/     4\       ||/       2   \    /     4\   4*x *tan(x)|      /       2   \     /     4\     |/       2   \    /     4\   4*x *tan(x)| |/       2   \    /     4\          8*x *tan(x)   4*x *\1 + tan (x)/   6*x *tan(x)|   144*x *tan(x)   48*x *\1 + tan (x)/        2    /       2   \    /     4\   24*x*tan(x)   36*x *\1 + tan (x)/   128*x *tan(x)   24*x *\1 + tan (x)/*tan(x)|
\1 + x /      *||\1 + tan (x)/*log\1 + x / + -----------|  + 2*\1 + tan (x)/ *log\1 + x / + 6*|\1 + tan (x)/*log\1 + x / + -----------|*|\1 + tan (x)/*log\1 + x /*tan(x) - ----------- + ------------------ + -----------| - ------------- - ------------------- + 4*tan (x)*\1 + tan (x)/*log\1 + x / + ----------- + ------------------- + ------------- + --------------------------|
               ||                                    4  |                                     |                                    4  | |                                            2               4                 4  |             2                  2                                                      4                 4                   3                    4          |
               |\                               1 + x   /                                     \                               1 + x   / |                                    /     4\           1 + x             1 + x   |     /     4\           /     4\                                                  1 + x             1 + x            /     4\                1 + x           |
               \                                                                                                                        \                                    \1 + x /                                     /     \1 + x /           \1 + x /                                                                                     \1 + x /                                /
(x4+1)tan⁡(x)(128x9tan⁡(x)(x4+1)3−48x6(tan⁡2(x)+1)(x4+1)2−144x5tan⁡(x)(x4+1)2+24x3(tan⁡2(x)+1)tan⁡(x)x4+1+36x2(tan⁡2(x)+1)x4+1+24xtan⁡(x)x4+1+(4x3tan⁡(x)x4+1+(tan⁡2(x)+1)log⁡(x4+1))3+6(4x3tan⁡(x)x4+1+(tan⁡2(x)+1)log⁡(x4+1))(−8x6tan⁡(x)(x4+1)2+4x3(tan⁡2(x)+1)x4+1+6x2tan⁡(x)x4+1+(tan⁡2(x)+1)log⁡(x4+1)tan⁡(x))+2(tan⁡2(x)+1)2log⁡(x4+1)+4(tan⁡2(x)+1)log⁡(x4+1)tan⁡2(x))\left(x^{4} + 1\right)^{\tan{\left(x \right)}} \left(\frac{128 x^{9} \tan{\left(x \right)}}{\left(x^{4} + 1\right)^{3}} - \frac{48 x^{6} \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{4} + 1\right)^{2}} - \frac{144 x^{5} \tan{\left(x \right)}}{\left(x^{4} + 1\right)^{2}} + \frac{24 x^{3} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{4} + 1} + \frac{36 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{4} + 1} + \frac{24 x \tan{\left(x \right)}}{x^{4} + 1} + \left(\frac{4 x^{3} \tan{\left(x \right)}}{x^{4} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 1 \right)}\right)^{3} + 6 \left(\frac{4 x^{3} \tan{\left(x \right)}}{x^{4} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 1 \right)}\right) \left(- \frac{8 x^{6} \tan{\left(x \right)}}{\left(x^{4} + 1\right)^{2}} + \frac{4 x^{3} \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{4} + 1} + \frac{6 x^{2} \tan{\left(x \right)}}{x^{4} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 1 \right)} \tan{\left(x \right)}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x^{4} + 1 \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 1 \right)} \tan^{2}{\left(x \right)}\right)
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Gráfico
Derivada de y=(x^4+1)^tgx
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