Sr Examen

Derivada de y=(tg2x)^arcsin3x

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

interior superior

Definida a trozos:

Solución

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

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
                  /                  /         2     \          \
   asin(3*x)      |3*log(tan(2*x))   \2 + 2*tan (2*x)/*asin(3*x)|
tan         (2*x)*|--------------- + ---------------------------|
                  |    __________              tan(2*x)         |
                  |   /        2                                |
                  \ \/  1 - 9*x                                 /
$$\left(\frac{\left(2 \tan^{2}{\left(2 x \right)} + 2\right) \operatorname{asin}{\left(3 x \right)}}{\tan{\left(2 x \right)}} + \frac{3 \log{\left(\tan{\left(2 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right) \tan^{\operatorname{asin}{\left(3 x \right)}}{\left(2 x \right)}$$
Segunda derivada [src]
                  /                                               2                                                  2                                                        \
                  |/                    /       2     \          \                                    /       2     \                   /       2     \                       |
   asin(3*x)      ||3*log(tan(2*x))   2*\1 + tan (2*x)/*asin(3*x)|      /       2     \             4*\1 + tan (2*x)/ *asin(3*x)     12*\1 + tan (2*x)/     27*x*log(tan(2*x))|
tan         (2*x)*||--------------- + ---------------------------|  + 8*\1 + tan (2*x)/*asin(3*x) - ---------------------------- + ---------------------- + ------------------|
                  ||    __________              tan(2*x)         |                                              2                     __________                        3/2   |
                  ||   /        2                                |                                           tan (2*x)               /        2               /       2\      |
                  \\ \/  1 - 9*x                                 /                                                                 \/  1 - 9*x  *tan(2*x)     \1 - 9*x /      /
$$\left(\frac{27 x \log{\left(\tan{\left(2 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \operatorname{asin}{\left(3 x \right)}}{\tan{\left(2 x \right)}} + \frac{3 \log{\left(\tan{\left(2 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right)^{2} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \operatorname{asin}{\left(3 x \right)}}{\tan^{2}{\left(2 x \right)}} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \operatorname{asin}{\left(3 x \right)} + \frac{12 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{\sqrt{1 - 9 x^{2}} \tan{\left(2 x \right)}}\right) \tan^{\operatorname{asin}{\left(3 x \right)}}{\left(2 x \right)}$$
Tercera derivada [src]
                  /                                               3                                                     /                                               2                                                        \                                                               2                       2                               3                                                                                                  \
                  |/                    /       2     \          \      /                    /       2     \          \ |                                /       2     \                   /       2     \                       |                         /       2     \        /       2     \         /       2     \                 /       2     \                                                           2                       /       2     \ |
   asin(3*x)      ||3*log(tan(2*x))   2*\1 + tan (2*x)/*asin(3*x)|      |3*log(tan(2*x))   2*\1 + tan (2*x)/*asin(3*x)| |  /       2     \             4*\1 + tan (2*x)/ *asin(3*x)     12*\1 + tan (2*x)/     27*x*log(tan(2*x))|   27*log(tan(2*x))   72*\1 + tan (2*x)/     36*\1 + tan (2*x)/      32*\1 + tan (2*x)/ *asin(3*x)   16*\1 + tan (2*x)/ *asin(3*x)      /       2     \                      729*x *log(tan(2*x))   162*x*\1 + tan (2*x)/ |
tan         (2*x)*||--------------- + ---------------------------|  + 3*|--------------- + ---------------------------|*|8*\1 + tan (2*x)/*asin(3*x) - ---------------------------- + ---------------------- + ------------------| + ---------------- + ------------------ - ----------------------- - ----------------------------- + ----------------------------- + 32*\1 + tan (2*x)/*asin(3*x)*tan(2*x) + -------------------- + ----------------------|
                  ||    __________              tan(2*x)         |      |    __________              tan(2*x)         | |                                          2                     __________                        3/2   |              3/2          __________         __________                        tan(2*x)                          3                                                                       5/2                 3/2         |
                  ||   /        2                                |      |   /        2                                | |                                       tan (2*x)               /        2               /       2\      |    /       2\            /        2         /        2     2                                                  tan (2*x)                                                        /       2\          /       2\            |
                  \\ \/  1 - 9*x                                 /      \ \/  1 - 9*x                                 / \                                                             \/  1 - 9*x  *tan(2*x)     \1 - 9*x /      /    \1 - 9*x /          \/  1 - 9*x        \/  1 - 9*x  *tan (2*x)                                                                                                              \1 - 9*x /          \1 - 9*x /   *tan(2*x)/
$$\left(\frac{729 x^{2} \log{\left(\tan{\left(2 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} + \frac{162 x \left(\tan^{2}{\left(2 x \right)} + 1\right)}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \tan{\left(2 x \right)}} + \left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \operatorname{asin}{\left(3 x \right)}}{\tan{\left(2 x \right)}} + \frac{3 \log{\left(\tan{\left(2 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right)^{3} + 3 \left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \operatorname{asin}{\left(3 x \right)}}{\tan{\left(2 x \right)}} + \frac{3 \log{\left(\tan{\left(2 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right) \left(\frac{27 x \log{\left(\tan{\left(2 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \operatorname{asin}{\left(3 x \right)}}{\tan^{2}{\left(2 x \right)}} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \operatorname{asin}{\left(3 x \right)} + \frac{12 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{\sqrt{1 - 9 x^{2}} \tan{\left(2 x \right)}}\right) + \frac{16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{3} \operatorname{asin}{\left(3 x \right)}}{\tan^{3}{\left(2 x \right)}} - \frac{32 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \operatorname{asin}{\left(3 x \right)}}{\tan{\left(2 x \right)}} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)} \operatorname{asin}{\left(3 x \right)} - \frac{36 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2}}{\sqrt{1 - 9 x^{2}} \tan^{2}{\left(2 x \right)}} + \frac{72 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{\sqrt{1 - 9 x^{2}}} + \frac{27 \log{\left(\tan{\left(2 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right) \tan^{\operatorname{asin}{\left(3 x \right)}}{\left(2 x \right)}$$
Gráfico
Derivada de y=(tg2x)^arcsin3x