Sr Examen

Otras calculadoras

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
     _________                 
    /  2    2     2     /x\    
x*\/  a  - x   + a *asin|-| - 5
                        \2/    
$$\left(a^{2} \operatorname{asin}{\left(\frac{x}{2} \right)} + x \sqrt{a^{2} - x^{2}}\right) - 5$$
x*sqrt(a^2 - x^2) + a^2*asin(x/2) - 5
Primera derivada [src]
   _________           2               2     
  /  2    2           a               x      
\/  a  - x   + --------------- - ------------
                      ________      _________
                     /      2      /  2    2 
                    /      x     \/  a  - x  
               2*  /   1 - --                
                 \/        4                 
$$\frac{a^{2}}{2 \sqrt{1 - \frac{x^{2}}{4}}} - \frac{x^{2}}{\sqrt{a^{2} - x^{2}}} + \sqrt{a^{2} - x^{2}}$$
Segunda derivada [src]
  /                       2               2     \
  |       3              x               a      |
x*|- ------------ - ------------ + -------------|
  |     _________            3/2             3/2|
  |    /  2    2    / 2    2\        /     2\   |
  |  \/  a  - x     \a  - x /        |    x |   |
  |                                8*|1 - --|   |
  \                                  \    4 /   /
$$x \left(\frac{a^{2}}{8 \left(1 - \frac{x^{2}}{4}\right)^{\frac{3}{2}}} - \frac{x^{2}}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{\sqrt{a^{2} - x^{2}}}\right)$$
Tercera derivada [src]
                        2              4              2              2  2    
       3             6*x            3*x              a            3*a *x     
- ------------ - ------------ - ------------ + ------------- + --------------
     _________            3/2            5/2             3/2              5/2
    /  2    2    / 2    2\      / 2    2\        /     2\         /     2\   
  \/  a  - x     \a  - x /      \a  - x /        |    x |         |    x |   
                                               8*|1 - --|      32*|1 - --|   
                                                 \    4 /         \    4 /   
$$\frac{3 a^{2} x^{2}}{32 \left(1 - \frac{x^{2}}{4}\right)^{\frac{5}{2}}} + \frac{a^{2}}{8 \left(1 - \frac{x^{2}}{4}\right)^{\frac{3}{2}}} - \frac{3 x^{4}}{\left(a^{2} - x^{2}\right)^{\frac{5}{2}}} - \frac{6 x^{2}}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{\sqrt{a^{2} - x^{2}}}$$