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Derivada de la función/ 2-x^2/ x/sqrt(a^2-x^2)/ x/sqrt(a^2-x^2)-asin(x/a)

Derivada de x/sqrt(a^2-x^2)-asin(x/a)

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

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Solución

Ha introducido [src] 
     x             /x\
------------ - asin|-|
   _________       \a/
  /  2    2           
\/  a  - x
xa2−x2−asin⁡(xa)\frac{x}{\sqrt{a^{2} - x^{2}}} - \operatorname{asin}{\left(\frac{x}{a} \right)} 
x/sqrt(a^2 - x^2) - asin(x/a)
Primera derivada [src] 
                     2                        
     1              x                1        
------------ + ------------ - ----------------
   _________            3/2           ________
  /  2    2    / 2    2\             /      2 
\/  a  - x     \a  - x /            /      x  
                              a*   /   1 - -- 
                                  /         2 
                                \/         a
x2(a2−x2)32+1a2−x2−1a1−x2a2\frac{x^{2}}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{a^{2} - x^{2}}} - \frac{1}{a \sqrt{1 - \frac{x^{2}}{a^{2}}}}
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Segunda derivada [src] 
  /                                       2    \
  |     3               1              3*x     |
x*|------------ - -------------- + ------------|
  |         3/2              3/2            5/2|
  |/ 2    2\         /     2\      / 2    2\   |
  |\a  - x /       3 |    x |      \a  - x /   |
  |               a *|1 - --|                  |
  |                  |     2|                  |
  \                  \    a /                  /
x(3x2(a2−x2)52+3(a2−x2)32−1a3(1−x2a2)32)x \left(\frac{3 x^{2}}{\left(a^{2} - x^{2}\right)^{\frac{5}{2}}} + \frac{3}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{a^{3} \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{3}{2}}}\right)
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Tercera derivada [src] 
                                       4              2               2     
     3               1             15*x           18*x             3*x      
------------ - -------------- + ------------ + ------------ - --------------
         3/2              3/2            7/2            5/2              5/2
/ 2    2\         /     2\      / 2    2\      / 2    2\         /     2\   
\a  - x /       3 |    x |      \a  - x /      \a  - x /       5 |    x |   
               a *|1 - --|                                    a *|1 - --|   
                  |     2|                                       |     2|   
                  \    a /                                       \    a /
15x4(a2−x2)72+18x2(a2−x2)52+3(a2−x2)32−1a3(1−x2a2)32−3x2a5(1−x2a2)52\frac{15 x^{4}}{\left(a^{2} - x^{2}\right)^{\frac{7}{2}}} + \frac{18 x^{2}}{\left(a^{2} - x^{2}\right)^{\frac{5}{2}}} + \frac{3}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{a^{3} \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{3}{2}}} - \frac{3 x^{2}}{a^{5} \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{5}{2}}}
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