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y=-arccos2x+x^2arcsin2x

Derivada de y=-arccos2x+x^2arcsin2x

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
              2          
-acos(2*x) + x *asin(2*x)
$$x^{2} \operatorname{asin}{\left(2 x \right)} - \operatorname{acos}{\left(2 x \right)}$$
-acos(2*x) + x^2*asin(2*x)
Gráfica
Primera derivada [src]
                                        2    
      2                              2*x     
------------- + 2*x*asin(2*x) + -------------
   __________                      __________
  /        2                      /        2 
\/  1 - 4*x                     \/  1 - 4*x  
$$\frac{2 x^{2}}{\sqrt{1 - 4 x^{2}}} + 2 x \operatorname{asin}{\left(2 x \right)} + \frac{2}{\sqrt{1 - 4 x^{2}}}$$
Segunda derivada [src]
  /                                        3                \
  |     4*x             4*x             4*x                 |
2*|------------- + ------------- + ------------- + asin(2*x)|
  |          3/2      __________             3/2            |
  |/       2\        /        2    /       2\               |
  \\1 - 4*x /      \/  1 - 4*x     \1 - 4*x /               /
$$2 \left(\frac{4 x^{3}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{4 x}{\sqrt{1 - 4 x^{2}}} + \frac{4 x}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \operatorname{asin}{\left(2 x \right)}\right)$$
Tercera derivada [src]
  /                    2            2             4   \
  |       2        14*x         24*x          24*x    |
4*|3 + -------- + -------- + ----------- + -----------|
  |           2          2             2             2|
  |    1 - 4*x    1 - 4*x    /       2\    /       2\ |
  \                          \1 - 4*x /    \1 - 4*x / /
-------------------------------------------------------
                        __________                     
                       /        2                      
                     \/  1 - 4*x                       
$$\frac{4 \left(\frac{24 x^{4}}{\left(1 - 4 x^{2}\right)^{2}} + \frac{14 x^{2}}{1 - 4 x^{2}} + \frac{24 x^{2}}{\left(1 - 4 x^{2}\right)^{2}} + 3 + \frac{2}{1 - 4 x^{2}}\right)}{\sqrt{1 - 4 x^{2}}}$$
Gráfico
Derivada de y=-arccos2x+x^2arcsin2x