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y=tg^32x*arcsinx^5

Derivada de y=tg^32x*arcsinx^5

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

Gráfico:

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Solución

Ha introducido [src]
   32        5   
tan  (x)*asin (x)
$$\tan^{32}{\left(x \right)} \operatorname{asin}^{5}{\left(x \right)}$$
tan(x)^32*asin(x)^5
Gráfica
Primera derivada [src]
                                            4       32   
    5       31    /           2   \   5*asin (x)*tan  (x)
asin (x)*tan  (x)*\32 + 32*tan (x)/ + -------------------
                                             ________    
                                            /      2     
                                          \/  1 - x      
$$\left(32 \tan^{2}{\left(x \right)} + 32\right) \tan^{31}{\left(x \right)} \operatorname{asin}^{5}{\left(x \right)} + \frac{5 \tan^{32}{\left(x \right)} \operatorname{asin}^{4}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
Segunda derivada [src]
                  /                                                                                        /       2   \               \
    3       30    |     2    /     4       x*asin(x) \          2    /       2   \ /           2   \   320*\1 + tan (x)/*asin(x)*tan(x)|
asin (x)*tan  (x)*|5*tan (x)*|- ------- + -----------| + 32*asin (x)*\1 + tan (x)/*\31 + 33*tan (x)/ + --------------------------------|
                  |          |        2           3/2|                                                              ________           |
                  |          |  -1 + x    /     2\   |                                                             /      2            |
                  \          \            \1 - x /   /                                                           \/  1 - x             /
$$\left(5 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{4}{x^{2} - 1}\right) \tan^{2}{\left(x \right)} + 32 \left(\tan^{2}{\left(x \right)} + 1\right) \left(33 \tan^{2}{\left(x \right)} + 31\right) \operatorname{asin}^{2}{\left(x \right)} + \frac{320 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \tan^{30}{\left(x \right)} \operatorname{asin}^{3}{\left(x \right)}$$
Tercera derivada [src]
                  /          /                    2          2     2                  \                             /                             2                           \                                                                         2    /       2   \ /           2   \       \
    2       29    |     3    |     12         asin (x)    3*x *asin (x)   12*x*asin(x)|          3    /       2   \ |     4          /       2   \          2    /       2   \|          2    /       2   \ /     4       x*asin(x) \           480*asin (x)*\1 + tan (x)/*\31 + 33*tan (x)/*tan(x)|
asin (x)*tan  (x)*|5*tan (x)*|----------- + ----------- + ------------- + ------------| + 64*asin (x)*\1 + tan (x)/*\2*tan (x) + 465*\1 + tan (x)/  + 94*tan (x)*\1 + tan (x)// + 480*tan (x)*\1 + tan (x)/*|- ------- + -----------|*asin(x) + ---------------------------------------------------|
                  |          |        3/2           3/2            5/2              2 |                                                                                                                     |        2           3/2|                                  ________                    |
                  |          |/     2\      /     2\       /     2\        /      2\  |                                                                                                                     |  -1 + x    /     2\   |                                 /      2                     |
                  \          \\1 - x /      \1 - x /       \1 - x /        \-1 + x /  /                                                                                                                     \            \1 - x /   /                               \/  1 - x                      /
$$\left(480 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{4}{x^{2} - 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} \operatorname{asin}{\left(x \right)} + 64 \left(\tan^{2}{\left(x \right)} + 1\right) \left(465 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 94 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 2 \tan^{4}{\left(x \right)}\right) \operatorname{asin}^{3}{\left(x \right)} + 5 \left(\frac{3 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{12 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{12}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \tan^{3}{\left(x \right)} + \frac{480 \left(\tan^{2}{\left(x \right)} + 1\right) \left(33 \tan^{2}{\left(x \right)} + 31\right) \tan{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \tan^{29}{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)}$$
Gráfico
Derivada de y=tg^32x*arcsinx^5