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Derivada de x*sqrt(a^2-x^2)+2*arcsin(x/a)-5

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Solución

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