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(x*x*x+1)^(tg2x)
Derivada de la función/ x*x+1/ x*x*x/ (x*x*x+1)^(tg2x)

Derivada de (x*x*x+1)^(tg2x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
           tan(2*x)
(x*x*x + 1)
(xxx+1)tan⁡(2x)\left(x x x + 1\right)^{\tan{\left(2 x \right)}} 
((x*x)*x + 1)^tan(2*x)
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-10102e29-1e29
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                    /                                   /   2      \         \
           tan(2*x) |/         2     \                  \2*x  + x*x/*tan(2*x)|
(x*x*x + 1)        *|\2 + 2*tan (2*x)/*log(x*x*x + 1) + ---------------------|
                    \                                         x*x*x + 1      /
(xxx+1)tan⁡(2x)((2x2+xx)tan⁡(2x)xxx+1+(2tan⁡2(2x)+2)log⁡(xxx+1))\left(x x x + 1\right)^{\tan{\left(2 x \right)}} \left(\frac{\left(2 x^{2} + x x\right) \tan{\left(2 x \right)}}{x x x + 1} + \left(2 \tan^{2}{\left(2 x \right)} + 2\right) \log{\left(x x x + 1 \right)}\right)
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Segunda derivada [src] 
                 /                                               2                                                                                                \
        tan(2*x) |/                                   2         \       4                                                                        2 /       2     \|
/     3\         ||  /       2     \    /     3\   3*x *tan(2*x)|    9*x *tan(2*x)   6*x*tan(2*x)     /       2     \    /     3\            12*x *\1 + tan (2*x)/|
\1 + x /        *||2*\1 + tan (2*x)/*log\1 + x / + -------------|  - ------------- + ------------ + 8*\1 + tan (2*x)/*log\1 + x /*tan(2*x) + ---------------------|
                 ||                                         3   |              2             3                                                            3       |
                 |\                                    1 + x    /      /     3\         1 + x                                                        1 + x        |
                 \                                                     \1 + x /                                                                                   /
(x3+1)tan⁡(2x)(−9x4tan⁡(2x)(x3+1)2+12x2(tan⁡2(2x)+1)x3+1+6xtan⁡(2x)x3+1+(3x2tan⁡(2x)x3+1+2(tan⁡2(2x)+1)log⁡(x3+1))2+8(tan⁡2(2x)+1)log⁡(x3+1)tan⁡(2x))\left(x^{3} + 1\right)^{\tan{\left(2 x \right)}} \left(- \frac{9 x^{4} \tan{\left(2 x \right)}}{\left(x^{3} + 1\right)^{2}} + \frac{12 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} + 1} + \frac{6 x \tan{\left(2 x \right)}}{x^{3} + 1} + \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} + 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)}\right)^{2} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} \tan{\left(2 x \right)}\right)
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Tercera derivada [src] 
                 /                                               3                                                                                                                                                                                                                                                                                                                                                                  \
        tan(2*x) |/                                   2         \      /                                   2         \ /     4                                                                        2 /       2     \\                                  2                   3                4 /       2     \                                                   /       2     \       6                2 /       2     \         |
/     3\         ||  /       2     \    /     3\   3*x *tan(2*x)|      |  /       2     \    /     3\   3*x *tan(2*x)| |  9*x *tan(2*x)   6*x*tan(2*x)     /       2     \    /     3\            12*x *\1 + tan (2*x)/|   6*tan(2*x)      /       2     \     /     3\   54*x *tan(2*x)   54*x *\1 + tan (2*x)/         2      /       2     \    /     3\   36*x*\1 + tan (2*x)/   54*x *tan(2*x)   72*x *\1 + tan (2*x)/*tan(2*x)|
\1 + x /        *||2*\1 + tan (2*x)/*log\1 + x / + -------------|  + 3*|2*\1 + tan (2*x)/*log\1 + x / + -------------|*|- ------------- + ------------ + 8*\1 + tan (2*x)/*log\1 + x /*tan(2*x) + ---------------------| + ---------- + 16*\1 + tan (2*x)/ *log\1 + x / - -------------- - --------------------- + 32*tan (2*x)*\1 + tan (2*x)/*log\1 + x / + -------------------- + -------------- + ------------------------------|
                 ||                                         3   |      |                                         3   | |            2             3                                                            3       |          3                                                 2                    2                                                                3                    3                       3            |
                 |\                                    1 + x    /      \                                    1 + x    / |    /     3\         1 + x                                                        1 + x        |     1 + x                                          /     3\             /     3\                                                            1 + x             /     3\                   1 + x             |
                 \                                                                                                     \    \1 + x /                                                                                   /                                                    \1 + x /             \1 + x /                                                                              \1 + x /                                     /
(x3+1)tan⁡(2x)(54x6tan⁡(2x)(x3+1)3−54x4(tan⁡2(2x)+1)(x3+1)2−54x3tan⁡(2x)(x3+1)2+72x2(tan⁡2(2x)+1)tan⁡(2x)x3+1+36x(tan⁡2(2x)+1)x3+1+(3x2tan⁡(2x)x3+1+2(tan⁡2(2x)+1)log⁡(x3+1))3+3(3x2tan⁡(2x)x3+1+2(tan⁡2(2x)+1)log⁡(x3+1))(−9x4tan⁡(2x)(x3+1)2+12x2(tan⁡2(2x)+1)x3+1+6xtan⁡(2x)x3+1+8(tan⁡2(2x)+1)log⁡(x3+1)tan⁡(2x))+16(tan⁡2(2x)+1)2log⁡(x3+1)+32(tan⁡2(2x)+1)log⁡(x3+1)tan⁡2(2x)+6tan⁡(2x)x3+1)\left(x^{3} + 1\right)^{\tan{\left(2 x \right)}} \left(\frac{54 x^{6} \tan{\left(2 x \right)}}{\left(x^{3} + 1\right)^{3}} - \frac{54 x^{4} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{\left(x^{3} + 1\right)^{2}} - \frac{54 x^{3} \tan{\left(2 x \right)}}{\left(x^{3} + 1\right)^{2}} + \frac{72 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)}}{x^{3} + 1} + \frac{36 x \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} + 1} + \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} + 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)}\right)^{3} + 3 \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} + 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)}\right) \left(- \frac{9 x^{4} \tan{\left(2 x \right)}}{\left(x^{3} + 1\right)^{2}} + \frac{12 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} + 1} + \frac{6 x \tan{\left(2 x \right)}}{x^{3} + 1} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} \tan{\left(2 x \right)}\right) + 16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x^{3} + 1 \right)} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} \tan^{2}{\left(2 x \right)} + \frac{6 \tan{\left(2 x \right)}}{x^{3} + 1}\right)
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Gráfico
Derivada de (x*x*x+1)^(tg2x)
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