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y=(x^3-1)^tg2x

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

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v

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 /                                                                                   /
$$\left(x^{3} - 1\right)^{\tan{\left(2 x \right)}} \left(- \frac{9 x^{4} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{2}} + \frac{12 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} - 1} + \frac{6 x \tan{\left(2 x \right)}}{x^{3} - 1} + \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} - 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)}\right)^{2} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)} \tan{\left(2 x \right)}\right)$$
3-я производная [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 /                                    /
$$\left(x^{3} - 1\right)^{\tan{\left(2 x \right)}} \left(\frac{54 x^{6} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{3}} - \frac{54 x^{4} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{\left(x^{3} - 1\right)^{2}} - \frac{54 x^{3} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{2}} + \frac{72 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)}}{x^{3} - 1} + \frac{36 x \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} - 1} + \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} - 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)}\right)^{3} + 3 \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} - 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)}\right) \left(- \frac{9 x^{4} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{2}} + \frac{12 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} - 1} + \frac{6 x \tan{\left(2 x \right)}}{x^{3} - 1} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)} \tan{\left(2 x \right)}\right) + 16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x^{3} - 1 \right)} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)} \tan^{2}{\left(2 x \right)} + \frac{6 \tan{\left(2 x \right)}}{x^{3} - 1}\right)$$
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