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y=(x^3+1)^tg2x

Derivada de y=(x^3+1)^tg2x

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
        tan(2*x)
/ 3    \        
\x  + 1/        
$$\left(x^{3} + 1\right)^{\tan{\left(2 x \right)}}$$
(x^3 + 1)^tan(2*x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
        tan(2*x) /                                   2         \
/ 3    \         |/         2     \    / 3    \   3*x *tan(2*x)|
\x  + 1/        *|\2 + 2*tan (2*x)/*log\x  + 1/ + -------------|
                 |                                     3       |
                 \                                    x  + 1   /
$$\left(x^{3} + 1\right)^{\tan{\left(2 x \right)}} \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} + 1} + \left(2 \tan^{2}{\left(2 x \right)} + 2\right) \log{\left(x^{3} + 1 \right)}\right)$$
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 /                                                                                   /
$$\left(x^{3} + 1\right)^{\tan{\left(2 x \right)}} \left(- \frac{9 x^{4} \tan{\left(2 x \right)}}{\left(x^{3} + 1\right)^{2}} + \frac{12 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} + 1} + \frac{6 x \tan{\left(2 x \right)}}{x^{3} + 1} + \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} + 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)}\right)^{2} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} \tan{\left(2 x \right)}\right)$$
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 /                                     /
$$\left(x^{3} + 1\right)^{\tan{\left(2 x \right)}} \left(\frac{54 x^{6} \tan{\left(2 x \right)}}{\left(x^{3} + 1\right)^{3}} - \frac{54 x^{4} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{\left(x^{3} + 1\right)^{2}} - \frac{54 x^{3} \tan{\left(2 x \right)}}{\left(x^{3} + 1\right)^{2}} + \frac{72 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)}}{x^{3} + 1} + \frac{36 x \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} + 1} + \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} + 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)}\right)^{3} + 3 \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} + 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)}\right) \left(- \frac{9 x^{4} \tan{\left(2 x \right)}}{\left(x^{3} + 1\right)^{2}} + \frac{12 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} + 1} + \frac{6 x \tan{\left(2 x \right)}}{x^{3} + 1} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} \tan{\left(2 x \right)}\right) + 16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x^{3} + 1 \right)} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} \tan^{2}{\left(2 x \right)} + \frac{6 \tan{\left(2 x \right)}}{x^{3} + 1}\right)$$
Gráfico
Derivada de y=(x^3+1)^tg2x