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xsqrt(1-x^2)*arccos(1-x^2)
Derivada de la función/ 1-x^2/ xsqrt/ arccos/ xsqrt(1-x^2)*arccos(1-x^2)

Derivada de xsqrt(1-x^2)*arccos(1-x^2)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
     ________             
    /      2      /     2\
x*\/  1 - x  *acos\1 - x /
x1−x2acos⁡(1−x2)x \sqrt{1 - x^{2}} \operatorname{acos}{\left(1 - x^{2} \right)} 
(x*sqrt(1 - x^2))*acos(1 - x^2)
Gráfica
02468-8-6-4-2-10102.5-2.5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                                     ________ 
/   ________         2    \                     2   /      2  
|  /      2         x     |     /     2\     2*x *\/  1 - x   
|\/  1 - x   - -----------|*acos\1 - x / + -------------------
|                 ________|                    _______________
|                /      2 |                   /             2 
\              \/  1 - x  /                  /      /     2\  
                                           \/   1 - \1 - x /
2x21−x21−(1−x2)2+(−x21−x2+1−x2)acos⁡(1−x2)\frac{2 x^{2} \sqrt{1 - x^{2}}}{\sqrt{1 - \left(1 - x^{2}\right)^{2}}} + \left(- \frac{x^{2}}{\sqrt{1 - x^{2}}} + \sqrt{1 - x^{2}}\right) \operatorname{acos}{\left(1 - x^{2} \right)}
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Segunda derivada [src] 
  /    /     ________         2    \                                      ________ /         2 /      2\\\
  |    |    /      2         x     |   /         2  \                    /      2  |      2*x *\-1 + x /||
  |  4*|- \/  1 - x   + -----------|   |        x   |     /     2\   2*\/  1 - x  *|-1 + ---------------||
  |    |                   ________|   |-3 + -------|*acos\1 - x /                 |                   2||
  |    |                  /      2 |   |           2|                              |          /      2\ ||
  |    \                \/  1 - x  /   \     -1 + x /                              \     -1 + \-1 + x / /|
x*|- ------------------------------- + --------------------------- - ------------------------------------|
  |            _______________                    ________                       _______________         |
  |           /             2                    /      2                       /             2          |
  |          /      /     2\                   \/  1 - x                       /      /     2\           |
  \        \/   1 - \1 - x /                                                 \/   1 - \1 - x /           /
x(−21−x2(2x2(x2−1)(x2−1)2−1−1)1−(1−x2)2−4(x21−x2−1−x2)1−(1−x2)2+(x2x2−1−3)acos⁡(1−x2)1−x2)x \left(- \frac{2 \sqrt{1 - x^{2}} \left(\frac{2 x^{2} \left(x^{2} - 1\right)}{\left(x^{2} - 1\right)^{2} - 1} - 1\right)}{\sqrt{1 - \left(1 - x^{2}\right)^{2}}} - \frac{4 \left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right)}{\sqrt{1 - \left(1 - x^{2}\right)^{2}}} + \frac{\left(\frac{x^{2}}{x^{2} - 1} - 3\right) \operatorname{acos}{\left(1 - x^{2} \right)}}{\sqrt{1 - x^{2}}}\right)
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Tercera derivada [src] 
                                                                                                             /                         2\                                  
                  2                  /         2 /      2\\ /     ________         2    \           ________ |              2 /      2\ |                                  
    /         2  \                   |      2*x *\-1 + x /| |    /      2         x     |      2   /      2  |       2   6*x *\-1 + x / |              /         2  \      
    |        x   |      /     2\   6*|-1 + ---------------|*|- \/  1 - x   + -----------|   4*x *\/  1 - x  *|3 - 5*x  + ---------------|            2 |        x   |      
  3*|-1 + -------| *acos\1 - x /     |                   2| |                   ________|                    |                         2|         6*x *|-3 + -------|      
    |           2|                   |          /      2\ | |                  /      2 |                    |                /      2\ |              |           2|      
    \     -1 + x /                   \     -1 + \-1 + x / / \                \/  1 - x  /                    \           -1 + \-1 + x / /              \     -1 + x /      
- ------------------------------ + ------------------------------------------------------ - --------------------------------------------- + -------------------------------
              ________                                  _______________                                                  3/2                                _______________
             /      2                                  /             2                                    /            2\                      ________    /             2 
           \/  1 - x                                  /      /     2\                                     |    /     2\ |                     /      2    /      /     2\  
                                                    \/   1 - \1 - x /                                     \1 - \1 - x / /                   \/  1 - x  *\/   1 - \1 - x /
−4x21−x2(6x2(x2−1)2(x2−1)2−1−5x2+3)(1−(1−x2)2)32+6x2(x2x2−1−3)1−x21−(1−x2)2+6(x21−x2−1−x2)(2x2(x2−1)(x2−1)2−1−1)1−(1−x2)2−3(x2x2−1−1)2acos⁡(1−x2)1−x2- \frac{4 x^{2} \sqrt{1 - x^{2}} \left(\frac{6 x^{2} \left(x^{2} - 1\right)^{2}}{\left(x^{2} - 1\right)^{2} - 1} - 5 x^{2} + 3\right)}{\left(1 - \left(1 - x^{2}\right)^{2}\right)^{\frac{3}{2}}} + \frac{6 x^{2} \left(\frac{x^{2}}{x^{2} - 1} - 3\right)}{\sqrt{1 - x^{2}} \sqrt{1 - \left(1 - x^{2}\right)^{2}}} + \frac{6 \left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right) \left(\frac{2 x^{2} \left(x^{2} - 1\right)}{\left(x^{2} - 1\right)^{2} - 1} - 1\right)}{\sqrt{1 - \left(1 - x^{2}\right)^{2}}} - \frac{3 \left(\frac{x^{2}}{x^{2} - 1} - 1\right)^{2} \operatorname{acos}{\left(1 - x^{2} \right)}}{\sqrt{1 - x^{2}}}
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Gráfico
Derivada de xsqrt(1-x^2)*arccos(1-x^2)
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