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Derivada de la función/ sin^4/ y=cos/ arcsin/ y=cos((arcsin^4)(5x^3))

Derivada de y=cos((arcsin^4)(5x^3))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   /    4       3\
cos\asin (x)*5*x /
cos⁡(5x3asin⁡4(x))\cos{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)} 
cos(asin(x)^4*(5*x^3))
Primera derivada [src] 
 /                     3     3   \                   
 |    2     4      20*x *asin (x)|    /    4       3\
-|15*x *asin (x) + --------------|*sin\asin (x)*5*x /
 |                     ________  |                   
 |                    /      2   |                   
 \                  \/  1 - x    /
−(20x3asin⁡3(x)1−x2+15x2asin⁡4(x))sin⁡(5x3asin⁡4(x))- \left(\frac{20 x^{3} \operatorname{asin}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 15 x^{2} \operatorname{asin}^{4}{\left(x \right)}\right) \sin{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)}
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Segunda derivada [src] 
              /  /                  2       3                       \                                                    2                            \
         2    |  |      2        6*x     2*x *asin(x)   12*x*asin(x)|    /   3     4   \      3 /                4*x    \      4       /   3     4   \|
-5*x*asin (x)*|2*|3*asin (x) - ------- + ------------ + ------------|*sin\5*x *asin (x)/ + 5*x *|3*asin(x) + -----------| *asin (x)*cos\5*x *asin (x)/|
              |  |                   2           3/2       ________ |                           |               ________|                             |
              |  |             -1 + x    /     2\         /      2  |                           |              /      2 |                             |
              \  \                       \1 - x /       \/  1 - x   /                           \            \/  1 - x  /                             /
−5x(5x3(4x1−x2+3asin⁡(x))2cos⁡(5x3asin⁡4(x))asin⁡4(x)+2(2x3asin⁡(x)(1−x2)32−6x2x2−1+12xasin⁡(x)1−x2+3asin⁡2(x))sin⁡(5x3asin⁡4(x)))asin⁡2(x)- 5 x \left(5 x^{3} \left(\frac{4 x}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}{\left(x \right)}\right)^{2} \cos{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)} \operatorname{asin}^{4}{\left(x \right)} + 2 \left(\frac{2 x^{3} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6 x^{2}}{x^{2} - 1} + \frac{12 x \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}^{2}{\left(x \right)}\right) \sin{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)}\right) \operatorname{asin}^{2}{\left(x \right)}
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Tercera derivada [src] 
  /    /                    3          2              5     2          4               3     2               2   \                                                     3                                                                        /                  2       3                       \                   \        
  |    |      3         12*x       54*x *asin(x)   6*x *asin (x)   18*x *asin(x)   20*x *asin (x)   36*x*asin (x)|    /   3     4   \       6 /                4*x    \      8       /   3     4   \       3     4    /                4*x    \ |      2        6*x     2*x *asin(x)   12*x*asin(x)|    /   3     4   \|        
5*|- 2*|3*asin (x) + ----------- - ------------- + ------------- + ------------- + -------------- + -------------|*sin\5*x *asin (x)/ + 25*x *|3*asin(x) + -----------| *asin (x)*sin\5*x *asin (x)/ - 30*x *asin (x)*|3*asin(x) + -----------|*|3*asin (x) - ------- + ------------ + ------------|*cos\5*x *asin (x)/|*asin(x)
  |    |                     3/2            2               5/2               2             3/2         ________ |                            |               ________|                                               |               ________| |                   2           3/2       ________ |                   |        
  |    |             /     2\         -1 + x        /     2\         /      2\      /     2\           /      2  |                            |              /      2 |                                               |              /      2 | |             -1 + x    /     2\         /      2  |                   |        
  \    \             \1 - x /                       \1 - x /         \-1 + x /      \1 - x /         \/  1 - x   /                            \            \/  1 - x  /                                               \            \/  1 - x  / \                       \1 - x /       \/  1 - x   /                   /
5(25x6(4x1−x2+3asin⁡(x))3sin⁡(5x3asin⁡4(x))asin⁡8(x)−30x3(4x1−x2+3asin⁡(x))(2x3asin⁡(x)(1−x2)32−6x2x2−1+12xasin⁡(x)1−x2+3asin⁡2(x))cos⁡(5x3asin⁡4(x))asin⁡4(x)−2(6x5asin⁡2(x)(1−x2)52+18x4asin⁡(x)(x2−1)2+20x3asin⁡2(x)(1−x2)32+12x3(1−x2)32−54x2asin⁡(x)x2−1+36xasin⁡2(x)1−x2+3asin⁡3(x))sin⁡(5x3asin⁡4(x)))asin⁡(x)5 \left(25 x^{6} \left(\frac{4 x}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}{\left(x \right)}\right)^{3} \sin{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)} \operatorname{asin}^{8}{\left(x \right)} - 30 x^{3} \left(\frac{4 x}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}{\left(x \right)}\right) \left(\frac{2 x^{3} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6 x^{2}}{x^{2} - 1} + \frac{12 x \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}^{2}{\left(x \right)}\right) \cos{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)} \operatorname{asin}^{4}{\left(x \right)} - 2 \left(\frac{6 x^{5} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{18 x^{4} \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{20 x^{3} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{12 x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{54 x^{2} \operatorname{asin}{\left(x \right)}}{x^{2} - 1} + \frac{36 x \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}^{3}{\left(x \right)}\right) \sin{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)}\right) \operatorname{asin}{\left(x \right)}
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