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y=(arcsin(x)-3x)/(√x^2+√1)

Derivada de y=(arcsin(x)-3x)/(√x^2+√1)

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

Gráfico:

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Solución

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