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y=arccos(1-x^2)^1/2

Derivada de y=arccos(1-x^2)^1/2

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

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Solución

Ha introducido [src]
   ______________
  /     /     2\ 
\/  acos\1 - x / 
$$\sqrt{\operatorname{acos}{\left(1 - x^{2} \right)}}$$
sqrt(acos(1 - x^2))
Gráfica
Primera derivada [src]
                  x                  
-------------------------------------
    _______________                  
   /             2     ______________
  /      /     2\     /     /     2\ 
\/   1 - \1 - x /  *\/  acos\1 - x / 
$$\frac{x}{\sqrt{1 - \left(1 - x^{2}\right)^{2}} \sqrt{\operatorname{acos}{\left(1 - x^{2} \right)}}}$$
Segunda derivada [src]
                                     2                      2 /      2\  
         1                          x                    2*x *\-1 + x /  
------------------- + ------------------------------ + ------------------
    _______________   /              2\                               3/2
   /             2    |     /      2\ |     /     2\   /            2\   
  /      /     2\     \-1 + \-1 + x / /*acos\1 - x /   |    /     2\ |   
\/   1 - \1 - x /                                      \1 - \1 - x / /   
-------------------------------------------------------------------------
                               ______________                            
                              /     /     2\                             
                            \/  acos\1 - x /                             
$$\frac{\frac{x^{2}}{\left(\left(x^{2} - 1\right)^{2} - 1\right) \operatorname{acos}{\left(1 - x^{2} \right)}} + \frac{2 x^{2} \left(x^{2} - 1\right)}{\left(1 - \left(1 - x^{2}\right)^{2}\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{1 - \left(1 - x^{2}\right)^{2}}}}{\sqrt{\operatorname{acos}{\left(1 - x^{2} \right)}}}$$
Tercera derivada [src]
  /                                                                                                                              2                                   \
  |                                           2               /      2\                        2                      2 /      2\                 2 /      2\        |
  |              3                         4*x              6*\-1 + x /                     3*x                   12*x *\-1 + x /              6*x *\-1 + x /        |
x*|------------------------------ + ------------------ + ------------------ + -------------------------------- + ------------------ - -------------------------------|
  |/              2\                               3/2                  3/2                  3/2                                5/2                    2             |
  ||     /      2\ |     /     2\   /            2\      /            2\      /            2\                    /            2\      /              2\              |
  |\-1 + \-1 + x / /*acos\1 - x /   |    /     2\ |      |    /     2\ |      |    /     2\ |        2/     2\   |    /     2\ |      |     /      2\ |      /     2\|
  \                                 \1 - \1 - x / /      \1 - \1 - x / /      \1 - \1 - x / /   *acos \1 - x /   \1 - \1 - x / /      \-1 + \-1 + x / / *acos\1 - x //
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                                                                             ______________                                                                           
                                                                            /     /     2\                                                                            
                                                                          \/  acos\1 - x /                                                                            
$$\frac{x \left(- \frac{6 x^{2} \left(x^{2} - 1\right)}{\left(\left(x^{2} - 1\right)^{2} - 1\right)^{2} \operatorname{acos}{\left(1 - x^{2} \right)}} + \frac{4 x^{2}}{\left(1 - \left(1 - x^{2}\right)^{2}\right)^{\frac{3}{2}}} + \frac{3 x^{2}}{\left(1 - \left(1 - x^{2}\right)^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(1 - x^{2} \right)}} + \frac{12 x^{2} \left(x^{2} - 1\right)^{2}}{\left(1 - \left(1 - x^{2}\right)^{2}\right)^{\frac{5}{2}}} + \frac{3}{\left(\left(x^{2} - 1\right)^{2} - 1\right) \operatorname{acos}{\left(1 - x^{2} \right)}} + \frac{6 \left(x^{2} - 1\right)}{\left(1 - \left(1 - x^{2}\right)^{2}\right)^{\frac{3}{2}}}\right)}{\sqrt{\operatorname{acos}{\left(1 - x^{2} \right)}}}$$
Gráfico
Derivada de y=arccos(1-x^2)^1/2