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(x*sqrt(2-x^2))/2-arcsin((x*sqrt(2))/2)

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

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