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y=(x^4-1)/(arcsin^32x)
Derivada de la función/ x^4-1/ sin^3/ arcsin/ y=(x^4-1)/(arcsin^32x)

Derivada de y=(x^4-1)/(arcsin^32x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   4      
  x  - 1  
----------
    3     
asin (2*x)
x4−1asin⁡3(2x)\frac{x^{4} - 1}{\operatorname{asin}^{3}{\left(2 x \right)}} 
(x^4 - 1)/asin(2*x)^3
Gráfica
02468-8-6-4-2-1010-50005000
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Trazar el gráfico f'(x)
Primera derivada [src] 
      3               / 4    \       
   4*x              6*\x  - 1/       
---------- - ------------------------
    3           __________           
asin (2*x)     /        2      4     
             \/  1 - 4*x  *asin (2*x)
4x3asin⁡3(2x)−6(x4−1)1−4x2asin⁡4(2x)\frac{4 x^{3}}{\operatorname{asin}^{3}{\left(2 x \right)}} - \frac{6 \left(x^{4} - 1\right)}{\sqrt{1 - 4 x^{2}} \operatorname{asin}^{4}{\left(2 x \right)}}
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Segunda derivada [src] 
   /                                 /      4\ /      x                   2          \\
   |                               2*\-1 + x /*|------------- + ---------------------||
   |                                           |          3/2   /        2\          ||
   |                  3                        |/       2\      \-1 + 4*x /*asin(2*x)||
   | 2             4*x                         \\1 - 4*x /                           /|
12*|x  - ----------------------- - ---------------------------------------------------|
   |        __________                                  asin(2*x)                     |
   |       /        2                                                                 |
   \     \/  1 - 4*x  *asin(2*x)                                                      /
---------------------------------------------------------------------------------------
                                           3                                           
                                       asin (2*x)
12(−4x31−4x2asin⁡(2x)+x2−2(x4−1)(x(1−4x2)32+2(4x2−1)asin⁡(2x))asin⁡(2x))asin⁡3(2x)\frac{12 \left(- \frac{4 x^{3}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}} + x^{2} - \frac{2 \left(x^{4} - 1\right) \left(\frac{x}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(4 x^{2} - 1\right) \operatorname{asin}{\left(2 x \right)}}\right)}{\operatorname{asin}{\left(2 x \right)}}\right)}{\operatorname{asin}^{3}{\left(2 x \right)}}
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Tercera derivada [src] 
   /              /                        2                                                        \                                                                          \
   |    /      4\ |      1             12*x                   20                       24*x         |       3 /      x                   2          \                          |
   |    \-1 + x /*|------------- + ------------- + ------------------------ - ----------------------|   12*x *|------------- + ---------------------|                          |
   |              |          3/2             5/2             3/2                         2          |         |          3/2   /        2\          |                          |
   |              |/       2\      /       2\      /       2\        2        /        2\           |         |/       2\      \-1 + 4*x /*asin(2*x)|                2         |
   |              \\1 - 4*x /      \1 - 4*x /      \1 - 4*x /   *asin (2*x)   \-1 + 4*x / *asin(2*x)/         \\1 - 4*x /                           /             9*x          |
24*|x - --------------------------------------------------------------------------------------------- - --------------------------------------------- - -----------------------|
   |                                              asin(2*x)                                                               asin(2*x)                        __________          |
   |                                                                                                                                                      /        2           |
   \                                                                                                                                                    \/  1 - 4*x  *asin(2*x)/
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                       3                                                                                        
                                                                                   asin (2*x)
24(−12x3(x(1−4x2)32+2(4x2−1)asin⁡(2x))asin⁡(2x)−9x21−4x2asin⁡(2x)+x−(x4−1)(12x2(1−4x2)52−24x(4x2−1)2asin⁡(2x)+1(1−4x2)32+20(1−4x2)32asin⁡2(2x))asin⁡(2x))asin⁡3(2x)\frac{24 \left(- \frac{12 x^{3} \left(\frac{x}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(4 x^{2} - 1\right) \operatorname{asin}{\left(2 x \right)}}\right)}{\operatorname{asin}{\left(2 x \right)}} - \frac{9 x^{2}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}} + x - \frac{\left(x^{4} - 1\right) \left(\frac{12 x^{2}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} - \frac{24 x}{\left(4 x^{2} - 1\right)^{2} \operatorname{asin}{\left(2 x \right)}} + \frac{1}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{20}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(2 x \right)}}\right)}{\operatorname{asin}{\left(2 x \right)}}\right)}{\operatorname{asin}^{3}{\left(2 x \right)}}
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Gráfico
Derivada de y=(x^4-1)/(arcsin^32x)
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