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y=cos^5x/arcsin8x
Derivada de la función/ sin8x/ cos^5x/ y=cos/ arcsin/ y=cos^5x/arcsin8x

Derivada de y=cos^5x/arcsin8x

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

Ha introducido [src] 
    5    
 cos (x) 
---------
asin(8*x)
cos⁡5(x)asin⁡(8x)\frac{\cos^{5}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}} 
cos(x)^5/asin(8*x)
Gráfica
02468-8-6-4-2-1010-2020
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Trazar el gráfico f'(x)
Primera derivada [src] 
               5                   4          
          8*cos (x)           5*cos (x)*sin(x)
- ------------------------- - ----------------
     ___________                 asin(8*x)    
    /         2      2                        
  \/  1 - 64*x  *asin (8*x)
−5sin⁡(x)cos⁡4(x)asin⁡(8x)−8cos⁡5(x)1−64x2asin⁡2(8x)- \frac{5 \sin{\left(x \right)} \cos^{4}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}} - \frac{8 \cos^{5}{\left(x \right)}}{\sqrt{1 - 64 x^{2}} \operatorname{asin}^{2}{\left(8 x \right)}}
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Segunda derivada [src] 
        /                                  2    /          1                   4*x      \                           \
        |                           128*cos (x)*|---------------------- + --------------|                           |
        |                                       |/         2\                        3/2|                           |
        |                                       |\-1 + 64*x /*asin(8*x)   /        2\   |                           |
   3    |       2            2                  \                         \1 - 64*x /   /       80*cos(x)*sin(x)    |
cos (x)*|- 5*cos (x) + 20*sin (x) - ----------------------------------------------------- + ------------------------|
        |                                                 asin(8*x)                            ___________          |
        |                                                                                     /         2           |
        \                                                                                   \/  1 - 64*x  *asin(8*x)/
---------------------------------------------------------------------------------------------------------------------
                                                      asin(8*x)
(−128(4x(1−64x2)32+1(64x2−1)asin⁡(8x))cos⁡2(x)asin⁡(8x)+20sin⁡2(x)−5cos⁡2(x)+80sin⁡(x)cos⁡(x)1−64x2asin⁡(8x))cos⁡3(x)asin⁡(8x)\frac{\left(- \frac{128 \left(\frac{4 x}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\left(64 x^{2} - 1\right) \operatorname{asin}{\left(8 x \right)}}\right) \cos^{2}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}} + 20 \sin^{2}{\left(x \right)} - 5 \cos^{2}{\left(x \right)} + \frac{80 \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{1 - 64 x^{2}} \operatorname{asin}{\left(8 x \right)}}\right) \cos^{3}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}}
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Tercera derivada [src] 
        /                                                     /                                                      2                              \                                                                                                     \
        |                                                3    |      1                      6                   192*x                  48*x         |                                                2    /          1                   4*x      \       |
        |                                         512*cos (x)*|-------------- + ------------------------- + -------------- - -----------------------|                                        1920*cos (x)*|---------------------- + --------------|*sin(x)|
        |                                                     |           3/2              3/2                         5/2               2          |                                                     |/         2\                        3/2|       |
        |                                                     |/        2\      /        2\        2        /        2\      /         2\           |       /     2           2   \                       |\-1 + 64*x /*asin(8*x)   /        2\   |       |
   2    |    /        2            2   \                      \\1 - 64*x /      \1 - 64*x /   *asin (8*x)   \1 - 64*x /      \-1 + 64*x / *asin(8*x)/   120*\- cos (x) + 4*sin (x)/*cos(x)                \                         \1 - 64*x /   /       |
cos (x)*|- 5*\- 13*cos (x) + 12*sin (x)/*sin(x) - --------------------------------------------------------------------------------------------------- - ---------------------------------- + -------------------------------------------------------------|
        |                                                                                      asin(8*x)                                                        ___________                                            asin(8*x)                          |
        |                                                                                                                                                      /         2                                                                                |
        \                                                                                                                                                    \/  1 - 64*x  *asin(8*x)                                                                     /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                         asin(8*x)
(1920(4x(1−64x2)32+1(64x2−1)asin⁡(8x))sin⁡(x)cos⁡2(x)asin⁡(8x)−5(12sin⁡2(x)−13cos⁡2(x))sin⁡(x)−512(192x2(1−64x2)52−48x(64x2−1)2asin⁡(8x)+1(1−64x2)32+6(1−64x2)32asin⁡2(8x))cos⁡3(x)asin⁡(8x)−120(4sin⁡2(x)−cos⁡2(x))cos⁡(x)1−64x2asin⁡(8x))cos⁡2(x)asin⁡(8x)\frac{\left(\frac{1920 \left(\frac{4 x}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\left(64 x^{2} - 1\right) \operatorname{asin}{\left(8 x \right)}}\right) \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}} - 5 \left(12 \sin^{2}{\left(x \right)} - 13 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} - \frac{512 \left(\frac{192 x^{2}}{\left(1 - 64 x^{2}\right)^{\frac{5}{2}}} - \frac{48 x}{\left(64 x^{2} - 1\right)^{2} \operatorname{asin}{\left(8 x \right)}} + \frac{1}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(8 x \right)}}\right) \cos^{3}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}} - \frac{120 \left(4 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}}{\sqrt{1 - 64 x^{2}} \operatorname{asin}{\left(8 x \right)}}\right) \cos^{2}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}}
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Gráfico
Derivada de y=cos^5x/arcsin8x
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