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y=√(arcsin(1/x^4))
Derivada de la función/ 1/x^4/ arcsin/ y=√(arcsin(1/x^4))

Derivada de y=√(arcsin(1/x^4))

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
     __________
    /     /1 \ 
   /  asin|--| 
  /       | 4| 
\/        \x /
asin⁡(1x4)\sqrt{\operatorname{asin}{\left(\frac{1}{x^{4}} \right)}} 
sqrt(asin(1/(x^4)))
Gráfica
02468-8-6-4-2-10105-5
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Primera derivada [src] 
              -2                
--------------------------------
        ________      __________
 5     /     1       /     /1 \ 
x *   /  1 - -- *   /  asin|--| 
     /        8    /       | 4| 
   \/        x   \/        \x /
−2x51−1x8asin⁡(1x4)- \frac{2}{x^{5} \sqrt{1 - \frac{1}{x^{8}}} \sqrt{\operatorname{asin}{\left(\frac{1}{x^{4}} \right)}}}
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Segunda derivada [src] 
  /      5               4                   2          \
2*|------------- + -------------- - --------------------|
  |     ________              3/2    4 /    1 \     /1 \|
  |    /     1      8 /    1 \      x *|1 - --|*asin|--||
  |   /  1 - --    x *|1 - --|         |     8|     | 4||
  |  /        8       |     8|         \    x /     \x /|
  \\/        x        \    x /                          /
---------------------------------------------------------
                            __________                   
                     6     /     /1 \                    
                    x *   /  asin|--|                    
                         /       | 4|                    
                       \/        \x /
2(51−1x8−2x4(1−1x8)asin⁡(1x4)+4x8(1−1x8)32)x6asin⁡(1x4)\frac{2 \left(\frac{5}{\sqrt{1 - \frac{1}{x^{8}}}} - \frac{2}{x^{4} \left(1 - \frac{1}{x^{8}}\right) \operatorname{asin}{\left(\frac{1}{x^{4}} \right)}} + \frac{4}{x^{8} \left(1 - \frac{1}{x^{8}}\right)^{\frac{3}{2}}}\right)}{x^{6} \sqrt{\operatorname{asin}{\left(\frac{1}{x^{4}} \right)}}}
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Tercera derivada [src] 
  /        15              38                24                    6                         12                      15         \
4*|- ------------- - -------------- - --------------- - ------------------------ + ---------------------- + --------------------|
  |       ________              3/2               5/2              3/2                         2             4 /    1 \     /1 \|
  |      /     1      8 /    1 \       16 /    1 \       8 /    1 \        2/1 \    12 /    1 \      /1 \   x *|1 - --|*asin|--||
  |     /  1 - --    x *|1 - --|      x  *|1 - --|      x *|1 - --|   *asin |--|   x  *|1 - --| *asin|--|      |     8|     | 4||
  |    /        8       |     8|          |     8|         |     8|         | 4|       |     8|      | 4|      \    x /     \x /|
  \  \/        x        \    x /          \    x /         \    x /         \x /       \    x /      \x /                       /
---------------------------------------------------------------------------------------------------------------------------------
                                                                __________                                                       
                                                         7     /     /1 \                                                        
                                                        x *   /  asin|--|                                                        
                                                             /       | 4|                                                        
                                                           \/        \x /
4(−151−1x8+15x4(1−1x8)asin⁡(1x4)−38x8(1−1x8)32−6x8(1−1x8)32asin⁡2(1x4)+12x12(1−1x8)2asin⁡(1x4)−24x16(1−1x8)52)x7asin⁡(1x4)\frac{4 \left(- \frac{15}{\sqrt{1 - \frac{1}{x^{8}}}} + \frac{15}{x^{4} \left(1 - \frac{1}{x^{8}}\right) \operatorname{asin}{\left(\frac{1}{x^{4}} \right)}} - \frac{38}{x^{8} \left(1 - \frac{1}{x^{8}}\right)^{\frac{3}{2}}} - \frac{6}{x^{8} \left(1 - \frac{1}{x^{8}}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(\frac{1}{x^{4}} \right)}} + \frac{12}{x^{12} \left(1 - \frac{1}{x^{8}}\right)^{2} \operatorname{asin}{\left(\frac{1}{x^{4}} \right)}} - \frac{24}{x^{16} \left(1 - \frac{1}{x^{8}}\right)^{\frac{5}{2}}}\right)}{x^{7} \sqrt{\operatorname{asin}{\left(\frac{1}{x^{4}} \right)}}}
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Gráfico
Derivada de y=√(arcsin(1/x^4))
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