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Derivada de x*sqrt(a^2-x^2)+a*arcsin(x/a)

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

Ha introducido [src]
     _________            
    /  2    2          /x\
x*\/  a  - x   + a*asin|-|
                       \a/
$$a \operatorname{asin}{\left(\frac{x}{a} \right)} + x \sqrt{a^{2} - x^{2}}$$
x*sqrt(a^2 - x^2) + a*asin(x/a)
Primera derivada [src]
                    _________         2     
      1            /  2    2         x      
-------------- + \/  a  - x   - ------------
      ________                     _________
     /      2                     /  2    2 
    /      x                    \/  a  - x  
   /   1 - --                               
  /         2                               
\/         a                                
$$- \frac{x^{2}}{\sqrt{a^{2} - x^{2}}} + \sqrt{a^{2} - x^{2}} + \frac{1}{\sqrt{1 - \frac{x^{2}}{a^{2}}}}$$
Segunda derivada [src]
  /                                        2     \
  |       3               1               x      |
x*|- ------------ + -------------- - ------------|
  |     _________              3/2            3/2|
  |    /  2    2       /     2\      / 2    2\   |
  |  \/  a  - x      2 |    x |      \a  - x /   |
  |                 a *|1 - --|                  |
  |                    |     2|                  |
  \                    \    a /                  /
$$x \left(- \frac{x^{2}}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{\sqrt{a^{2} - x^{2}}} + \frac{1}{a^{2} \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{3}{2}}}\right)$$
Tercera derivada [src]
                                         2              4               2     
       3               1              6*x            3*x             3*x      
- ------------ + -------------- - ------------ - ------------ + --------------
     _________              3/2            3/2            5/2              5/2
    /  2    2       /     2\      / 2    2\      / 2    2\         /     2\   
  \/  a  - x      2 |    x |      \a  - x /      \a  - x /       4 |    x |   
                 a *|1 - --|                                    a *|1 - --|   
                    |     2|                                       |     2|   
                    \    a /                                       \    a /   
$$- \frac{3 x^{4}}{\left(a^{2} - x^{2}\right)^{\frac{5}{2}}} - \frac{6 x^{2}}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{\sqrt{a^{2} - x^{2}}} + \frac{1}{a^{2} \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{3}{2}}} + \frac{3 x^{2}}{a^{4} \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{5}{2}}}$$