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x+sqrt(1-xx)arcsin(x)

Derivada de x+sqrt(1-xx)arcsin(x)

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

Ha introducido [src]
      _________        
x + \/ 1 - x*x *asin(x)
$$x + \sqrt{- x x + 1} \operatorname{asin}{\left(x \right)}$$
x + sqrt(1 - x*x)*asin(x)
Gráfica
Primera derivada [src]
      _________              
    \/ 1 - x*x     x*asin(x) 
1 + ----------- - -----------
       ________     _________
      /      2    \/ 1 - x*x 
    \/  1 - x                
$$- \frac{x \operatorname{asin}{\left(x \right)}}{\sqrt{- x x + 1}} + 1 + \frac{\sqrt{- x x + 1}}{\sqrt{1 - x^{2}}}$$
Segunda derivada [src]
 /                         2        \
 |  x        asin(x)      x *asin(x)|
-|------ + ----------- + -----------|
 |     2      ________           3/2|
 |1 - x      /      2    /     2\   |
 \         \/  1 - x     \1 - x /   /
$$- (\frac{x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{x}{1 - x^{2}} + \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}})$$
Tercera derivada [src]
 /               2                      3        \
 |  2         3*x      3*x*asin(x)   3*x *asin(x)|
-|------ + --------- + ----------- + ------------|
 |     2           2           3/2           5/2 |
 |1 - x    /     2\    /     2\      /     2\    |
 \         \1 - x /    \1 - x /      \1 - x /    /
$$- (\frac{3 x^{3} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x^{2}}{\left(1 - x^{2}\right)^{2}} + \frac{3 x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{1 - x^{2}})$$
Gráfico
Derivada de x+sqrt(1-xx)arcsin(x)