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y=ln^2(arcsinx-x)
Derivada de la función/ y=ln^2/ arcsin/ y=ln^2(arcsinx-x)

Derivada de y=ln^2(arcsinx-x)

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

Ha introducido [src] 
   2             
log (asin(x) - x)
log⁡(−x+asin⁡(x))2\log{\left(- x + \operatorname{asin}{\left(x \right)} \right)}^{2} 
log(asin(x) - x)^2
Gráfica
02468-8-6-4-2-1010-1000500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  /          1     \                 
2*|-1 + -----------|*log(asin(x) - x)
  |        ________|                 
  |       /      2 |                 
  \     \/  1 - x  /                 
-------------------------------------
             asin(x) - x
2(−1+11−x2)log⁡(−x+asin⁡(x))−x+asin⁡(x)\frac{2 \left(-1 + \frac{1}{\sqrt{1 - x^{2}}}\right) \log{\left(- x + \operatorname{asin}{\left(x \right)} \right)}}{- x + \operatorname{asin}{\left(x \right)}}
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Segunda derivada [src] 
  /                 2                                          2                  \
  |/         1     \                          /         1     \                   |
  ||1 - -----------|                          |1 - -----------| *log(-x + asin(x))|
  ||       ________|                          |       ________|                   |
  ||      /      2 |                          |      /      2 |                   |
  |\    \/  1 - x  /    x*log(-x + asin(x))   \    \/  1 - x  /                   |
2*|------------------ - ------------------- - ------------------------------------|
  |   x - asin(x)                   3/2                   x - asin(x)             |
  |                         /     2\                                              |
  \                         \1 - x /                                              /
-----------------------------------------------------------------------------------
                                    x - asin(x)
2(−xlog⁡(−x+asin⁡(x))(1−x2)32−(1−11−x2)2log⁡(−x+asin⁡(x))x−asin⁡(x)+(1−11−x2)2x−asin⁡(x))x−asin⁡(x)\frac{2 \left(- \frac{x \log{\left(- x + \operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{\left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{2} \log{\left(- x + \operatorname{asin}{\left(x \right)} \right)}}{x - \operatorname{asin}{\left(x \right)}} + \frac{\left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{2}}{x - \operatorname{asin}{\left(x \right)}}\right)}{x - \operatorname{asin}{\left(x \right)}}
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Tercera derivada [src] 
  /                                         3                                               3                                                                                        \
  |                        /         1     \                               /         1     \                            /         1     \         /         1     \                  |
  |                      3*|1 - -----------|                             2*|1 - -----------| *log(-x + asin(x))     3*x*|1 - -----------|     3*x*|1 - -----------|*log(-x + asin(x))|
  |                        |       ________|                               |       ________|                            |       ________|         |       ________|                  |
  |                        |      /      2 |       2                       |      /      2 |                            |      /      2 |         |      /      2 |                  |
  |  log(-x + asin(x))     \    \/  1 - x  /    3*x *log(-x + asin(x))     \    \/  1 - x  /                            \    \/  1 - x  /         \    \/  1 - x  /                  |
2*|- ----------------- - -------------------- - ---------------------- + -------------------------------------- - ------------------------- + ---------------------------------------|
  |             3/2                      2                   5/2                                  2                       3/2                                3/2                     |
  |     /     2\            (x - asin(x))            /     2\                        (x - asin(x))                /     2\                           /     2\                        |
  \     \1 - x /                                     \1 - x /                                                     \1 - x /   *(x - asin(x))          \1 - x /   *(x - asin(x))       /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                     x - asin(x)
2(−3x2log⁡(−x+asin⁡(x))(1−x2)52+3x(1−11−x2)log⁡(−x+asin⁡(x))(1−x2)32(x−asin⁡(x))−3x(1−11−x2)(1−x2)32(x−asin⁡(x))+2(1−11−x2)3log⁡(−x+asin⁡(x))(x−asin⁡(x))2−3(1−11−x2)3(x−asin⁡(x))2−log⁡(−x+asin⁡(x))(1−x2)32)x−asin⁡(x)\frac{2 \left(- \frac{3 x^{2} \log{\left(- x + \operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right) \log{\left(- x + \operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x - \operatorname{asin}{\left(x \right)}\right)} - \frac{3 x \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x - \operatorname{asin}{\left(x \right)}\right)} + \frac{2 \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{3} \log{\left(- x + \operatorname{asin}{\left(x \right)} \right)}}{\left(x - \operatorname{asin}{\left(x \right)}\right)^{2}} - \frac{3 \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{3}}{\left(x - \operatorname{asin}{\left(x \right)}\right)^{2}} - \frac{\log{\left(- x + \operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)}{x - \operatorname{asin}{\left(x \right)}}
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Gráfico
Derivada de y=ln^2(arcsinx-x)
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