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y=3^(0.5)*arcsin((1-x^2)^0.5)

Derivada de y=3^(0.5)*arcsin((1-x^2)^0.5)

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

Ha introducido [src]
          /   ________\
  ___     |  /      2 |
\/ 3 *asin\\/  1 - x  /
$$\sqrt{3} \operatorname{asin}{\left(\sqrt{1 - x^{2}} \right)}$$
sqrt(3)*asin(sqrt(1 - x^2))
Gráfica
Primera derivada [src]
        ___    
   -x*\/ 3     
---------------
   ________    
  /      2     
\/  1 - x  *|x|
$$- \frac{\sqrt{3} x}{\sqrt{1 - x^{2}} \left|{x}\right|}$$
Segunda derivada [src]
       /                       2     \ 
   ___ | 1    sign(x)         x      | 
-\/ 3 *|--- - ------- - -------------| 
       ||x|      x      /      2\    | 
       \                \-1 + x /*|x|/ 
---------------------------------------
                 ________              
                /      2               
              \/  1 - x                
$$- \frac{\sqrt{3} \left(- \frac{x^{2}}{\left(x^{2} - 1\right) \left|{x}\right|} + \frac{1}{\left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x}\right)}{\sqrt{1 - x^{2}}}$$
Tercera derivada [src]
       /                                                        3     \ 
   ___ |  2*DiracDelta(x)   2*sign(x)        3*x             3*x      | 
-\/ 3 *|- --------------- + --------- - ------------- + --------------| 
       |         x                 2    /      2\                2    | 
       |                     -1 + x     \-1 + x /*|x|   /      2\     | 
       \                                                \-1 + x / *|x|/ 
------------------------------------------------------------------------
                                 ________                               
                                /      2                                
                              \/  1 - x                                 
$$- \frac{\sqrt{3} \left(\frac{3 x^{3}}{\left(x^{2} - 1\right)^{2} \left|{x}\right|} - \frac{3 x}{\left(x^{2} - 1\right) \left|{x}\right|} + \frac{2 \operatorname{sign}{\left(x \right)}}{x^{2} - 1} - \frac{2 \delta\left(x\right)}{x}\right)}{\sqrt{1 - x^{2}}}$$
Gráfico
Derivada de y=3^(0.5)*arcsin((1-x^2)^0.5)