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

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

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

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Solución

Ha introducido [src] 
     _________                 
    /  2    2     2     /x\    
x*\/  a  - x   + a *asin|-| - 5
                        \a/
(a2asin⁡(xa)+xa2−x2)−5\left(a^{2} \operatorname{asin}{\left(\frac{x}{a} \right)} + x \sqrt{a^{2} - x^{2}}\right) - 5 
x*sqrt(a^2 - x^2) + a^2*asin(x/a) - 5
Primera derivada [src] 
   _________                          2     
  /  2    2          a               x      
\/  a  - x   + -------------- - ------------
                     ________      _________
                    /      2      /  2    2 
                   /      x     \/  a  - x  
                  /   1 - --                
                 /         2                
               \/         a
a1−x2a2−x2a2−x2+a2−x2\frac{a}{\sqrt{1 - \frac{x^{2}}{a^{2}}}} - \frac{x^{2}}{\sqrt{a^{2} - x^{2}}} + \sqrt{a^{2} - x^{2}}
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Segunda derivada [src] 
  /                                       2     \
  |       3               1              x      |
x*|- ------------ + ------------- - ------------|
  |     _________             3/2            3/2|
  |    /  2    2      /     2\      / 2    2\   |
  |  \/  a  - x       |    x |      \a  - x /   |
  |                 a*|1 - --|                  |
  |                   |     2|                  |
  \                   \    a /                  /
x(−x2(a2−x2)32−3a2−x2+1a(1−x2a2)32)x \left(- \frac{x^{2}}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{\sqrt{a^{2} - x^{2}}} + \frac{1}{a \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{3}{2}}}\right)
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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       |    x |      \a  - x /      \a  - x /       3 |    x |   
                 a*|1 - --|                                    a *|1 - --|   
                   |     2|                                       |     2|   
                   \    a /                                       \    a /
−3x4(a2−x2)52−6x2(a2−x2)32−3a2−x2+1a(1−x2a2)32+3x2a3(1−x2a2)52- \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 \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{3}{2}}} + \frac{3 x^{2}}{a^{3} \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{5}{2}}}
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