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Derivada de la función/ y=x/2*√(a²-x²)+a²/2*arcsinx/2

Derivada de y=x/2*√(a²-x²)+a²/2*arcsinx/2

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

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Solución

Ha introducido [src] 
                  2        
                 a         
     _________   --*asin(x)
x   /  2    2    2         
-*\/  a  - x   + ----------
2                    2
x2a2−x2+a22asin⁡(x)2\frac{x}{2} \sqrt{a^{2} - x^{2}} + \frac{\frac{a^{2}}{2} \operatorname{asin}{\left(x \right)}}{2} 
(x/2)*sqrt(a^2 - x^2) + ((a^2/2)*asin(x))/2
Primera derivada [src] 
   _________                                 
  /  2    2           2                2     
\/  a  - x           x                a      
------------ - -------------- + -------------
     2              _________        ________
                   /  2    2        /      2 
               2*\/  a  - x     4*\/  1 - x
a241−x2−x22a2−x2+a2−x22\frac{a^{2}}{4 \sqrt{1 - x^{2}}} - \frac{x^{2}}{2 \sqrt{a^{2} - x^{2}}} + \frac{\sqrt{a^{2} - x^{2}}}{2}
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Segunda derivada [src] 
  /                       2              2    \
  |       6              a            2*x     |
x*|- ------------ + ----------- - ------------|
  |     _________           3/2            3/2|
  |    /  2    2    /     2\      / 2    2\   |
  \  \/  a  - x     \1 - x /      \a  - x /   /
-----------------------------------------------
                       4
x(a2(1−x2)32−2x2(a2−x2)32−6a2−x2)4\frac{x \left(\frac{a^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 x^{2}}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} - \frac{6}{\sqrt{a^{2} - x^{2}}}\right)}{4}
Simplificar
Tercera derivada [src] 
                          2               4               2              2  2   
        3              3*x             3*x               a            3*a *x    
- -------------- - ------------ - -------------- + ------------- + -------------
       _________            3/2              5/2             3/2             5/2
      /  2    2    / 2    2\        / 2    2\        /     2\        /     2\   
  2*\/  a  - x     \a  - x /      2*\a  - x /      4*\1 - x /      4*\1 - x /
3a2x24(1−x2)52+a24(1−x2)32−3x42(a2−x2)52−3x2(a2−x2)32−32a2−x2\frac{3 a^{2} x^{2}}{4 \left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{a^{2}}{4 \left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3 x^{4}}{2 \left(a^{2} - x^{2}\right)^{\frac{5}{2}}} - \frac{3 x^{2}}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{2 \sqrt{a^{2} - x^{2}}}
Simplificar
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