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y=tg^(5)*3x*arcsin(5x)
Derivada de la función/ arcsin/ sin(5x)/ y=tg^(5)*3x*arcsin(5x)

Derivada de y=tg^(5)*3x*arcsin(5x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   5                 
tan (3*x*asin(x))*5*x
5xtan⁡5(3xasin⁡(x))5 x \tan^{5}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} 
tan((3*x)*asin(x))^5*(5*x)
Gráfica
02468-8-6-4-2-1010200000000-100000000
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Primera derivada [src] 
     5                        4              /       2             \ /                3*x    \
5*tan (3*x*asin(x)) + 25*x*tan (3*x*asin(x))*\1 + tan (3*x*asin(x))/*|3*asin(x) + -----------|
                                                                     |               ________|
                                                                     |              /      2 |
                                                                     \            \/  1 - x  /
25x(3x1−x2+3asin⁡(x))(tan⁡2(3xasin⁡(x))+1)tan⁡4(3xasin⁡(x))+5tan⁡5(3xasin⁡(x))25 x \left(\frac{3 x}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}{\left(x \right)}\right) \left(\tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} + 1\right) \tan^{4}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} + 5 \tan^{5}{\left(3 x \operatorname{asin}{\left(x \right)} \right)}
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Segunda derivada [src] 
                                             /  /                                                                                                     /         2  \                 \                                             \
                                             |  |                                                                                                     |        x   |                 |                                             |
                                             |  |                                                                                                     |-2 + -------|*tan(3*x*asin(x))|                                             |
                                             |  |                         2                                               2                           |           2|                 |                                             |
      3              /       2             \ |  |  /     x               \     2                   /     x               \  /       2             \   \     -1 + x /                 |     /     x               \                 |
75*tan (3*x*asin(x))*\1 + tan (3*x*asin(x))/*|x*|6*|----------- + asin(x)| *tan (3*x*asin(x)) + 12*|----------- + asin(x)| *\1 + tan (3*x*asin(x))/ - -------------------------------| + 2*|----------- + asin(x)|*tan(3*x*asin(x))|
                                             |  |  |   ________          |                         |   ________          |                                         ________          |     |   ________          |                 |
                                             |  |  |  /      2           |                         |  /      2           |                                        /      2           |     |  /      2           |                 |
                                             \  \  \\/  1 - x            /                         \\/  1 - x            /                                      \/  1 - x            /     \\/  1 - x            /                 /
75(x(12(x1−x2+asin⁡(x))2(tan⁡2(3xasin⁡(x))+1)+6(x1−x2+asin⁡(x))2tan⁡2(3xasin⁡(x))−(x2x2−1−2)tan⁡(3xasin⁡(x))1−x2)+2(x1−x2+asin⁡(x))tan⁡(3xasin⁡(x)))(tan⁡2(3xasin⁡(x))+1)tan⁡3(3xasin⁡(x))75 \left(x \left(12 \left(\frac{x}{\sqrt{1 - x^{2}}} + \operatorname{asin}{\left(x \right)}\right)^{2} \left(\tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} + 1\right) + 6 \left(\frac{x}{\sqrt{1 - x^{2}}} + \operatorname{asin}{\left(x \right)}\right)^{2} \tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} - \frac{\left(\frac{x^{2}}{x^{2} - 1} - 2\right) \tan{\left(3 x \operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}}\right) + 2 \left(\frac{x}{\sqrt{1 - x^{2}}} + \operatorname{asin}{\left(x \right)}\right) \tan{\left(3 x \operatorname{asin}{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} + 1\right) \tan^{3}{\left(3 x \operatorname{asin}{\left(x \right)} \right)}
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Tercera derivada [src] 
                                             /    /                                                                                                                                                                                                                                             /         2  \                                                      /         2  \                                         \                                                                                                                                                            \
                                             |    |                                                                                                                                                                                                       /          2 \         3              |        x   | /     x               \      /       2             \ |        x   | /     x               \                 |     /                                                                                                     /         2  \                 \                 |
                                             |    |                                                                                                                                                                                        2              |       3*x  |   18*tan (3*x*asin(x))*|-2 + -------|*|----------- + asin(x)|   36*\1 + tan (3*x*asin(x))/*|-2 + -------|*|----------- + asin(x)|*tan(3*x*asin(x))|     |                                                                                                     |        x   |                 |                 |
                                             |    |                                                                                                                                                                                   x*tan (3*x*asin(x))*|-4 + -------|                        |           2| |   ________          |                              |           2| |   ________          |                 |     |                                                                                                     |-2 + -------|*tan(3*x*asin(x))|                 |
                                             |    |                             2                        3                             3                                                3                                                                 |           2|                        \     -1 + x / |  /      2           |                              \     -1 + x / |  /      2           |                 |     |                         2                                               2                           |           2|                 |                 |
      2              /       2             \ |    |      /       2             \  /     x               \       /     x               \     4                    /     x               \     2              /       2             \                       \     -1 + x /                                       \\/  1 - x            /                                             \\/  1 - x            /                 |     |  /     x               \     2                   /     x               \  /       2             \   \     -1 + x /                 |                 |
75*tan (3*x*asin(x))*\1 + tan (3*x*asin(x))/*|- x*|- 108*\1 + tan (3*x*asin(x))/ *|----------- + asin(x)|  - 36*|----------- + asin(x)| *tan (3*x*asin(x)) - 234*|----------- + asin(x)| *tan (3*x*asin(x))*\1 + tan (3*x*asin(x))/ + ---------------------------------- + ----------------------------------------------------------- + ----------------------------------------------------------------------------------| + 3*|6*|----------- + asin(x)| *tan (3*x*asin(x)) + 12*|----------- + asin(x)| *\1 + tan (3*x*asin(x))/ - -------------------------------|*tan(3*x*asin(x))|
                                             |    |                               |   ________          |       |   ________          |                          |   ________          |                                                                 3/2                                          ________                                                                 ________                                    |     |  |   ________          |                         |   ________          |                                         ________          |                 |
                                             |    |                               |  /      2           |       |  /      2           |                          |  /      2           |                                                         /     2\                                            /      2                                                                 /      2                                     |     |  |  /      2           |                         |  /      2           |                                        /      2           |                 |
                                             \    \                               \\/  1 - x            /       \\/  1 - x            /                          \\/  1 - x            /                                                         \1 - x /                                          \/  1 - x                                                                \/  1 - x                                      /     \  \\/  1 - x            /                         \\/  1 - x            /                                      \/  1 - x            /                 /
75(−x(x(3x2x2−1−4)tan⁡2(3xasin⁡(x))(1−x2)32−108(x1−x2+asin⁡(x))3(tan⁡2(3xasin⁡(x))+1)2−234(x1−x2+asin⁡(x))3(tan⁡2(3xasin⁡(x))+1)tan⁡2(3xasin⁡(x))−36(x1−x2+asin⁡(x))3tan⁡4(3xasin⁡(x))+36(x1−x2+asin⁡(x))(x2x2−1−2)(tan⁡2(3xasin⁡(x))+1)tan⁡(3xasin⁡(x))1−x2+18(x1−x2+asin⁡(x))(x2x2−1−2)tan⁡3(3xasin⁡(x))1−x2)+3(12(x1−x2+asin⁡(x))2(tan⁡2(3xasin⁡(x))+1)+6(x1−x2+asin⁡(x))2tan⁡2(3xasin⁡(x))−(x2x2−1−2)tan⁡(3xasin⁡(x))1−x2)tan⁡(3xasin⁡(x)))(tan⁡2(3xasin⁡(x))+1)tan⁡2(3xasin⁡(x))75 \left(- x \left(\frac{x \left(\frac{3 x^{2}}{x^{2} - 1} - 4\right) \tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - 108 \left(\frac{x}{\sqrt{1 - x^{2}}} + \operatorname{asin}{\left(x \right)}\right)^{3} \left(\tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} + 1\right)^{2} - 234 \left(\frac{x}{\sqrt{1 - x^{2}}} + \operatorname{asin}{\left(x \right)}\right)^{3} \left(\tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} + 1\right) \tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} - 36 \left(\frac{x}{\sqrt{1 - x^{2}}} + \operatorname{asin}{\left(x \right)}\right)^{3} \tan^{4}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} + \frac{36 \left(\frac{x}{\sqrt{1 - x^{2}}} + \operatorname{asin}{\left(x \right)}\right) \left(\frac{x^{2}}{x^{2} - 1} - 2\right) \left(\tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} + 1\right) \tan{\left(3 x \operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}} + \frac{18 \left(\frac{x}{\sqrt{1 - x^{2}}} + \operatorname{asin}{\left(x \right)}\right) \left(\frac{x^{2}}{x^{2} - 1} - 2\right) \tan^{3}{\left(3 x \operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}}\right) + 3 \left(12 \left(\frac{x}{\sqrt{1 - x^{2}}} + \operatorname{asin}{\left(x \right)}\right)^{2} \left(\tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} + 1\right) + 6 \left(\frac{x}{\sqrt{1 - x^{2}}} + \operatorname{asin}{\left(x \right)}\right)^{2} \tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} - \frac{\left(\frac{x^{2}}{x^{2} - 1} - 2\right) \tan{\left(3 x \operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \tan{\left(3 x \operatorname{asin}{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)} + 1\right) \tan^{2}{\left(3 x \operatorname{asin}{\left(x \right)} \right)}
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Gráfico
Derivada de y=tg^(5)*3x*arcsin(5x)
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