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ln(arcsin(2x-(x^2)))
The derivative of the function/ ln(arcsin(2x-(x^2)))

Derivative of ln(arcsin(2x-(x^2)))

Function f() - derivative -N order at the point
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You have entered [src] 
   /    /       2\\
log\asin\2*x - x //
log⁡(asin⁡(−x2+2x))\log{\left(\operatorname{asin}{\left(- x^{2} + 2 x \right)} \right)}
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The graph
02468-8-6-4-2-1010-2525
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The first derivative [src] 
              2 - 2*x               
------------------------------------
    _________________               
   /               2                
  /      /       2\       /       2\
\/   1 - \2*x - x /  *asin\2*x - x /
2−2x1−(−x2+2x)2asin⁡(−x2+2x)\frac{2 - 2 x}{\sqrt{1 - \left(- x^{2} + 2 x\right)^{2}} \operatorname{asin}{\left(- x^{2} + 2 x \right)}}
Simplify
The second derivative [src] 
  /                                             2                            2         \
  |         1                         2*(-1 + x)                 2*x*(-1 + x) *(-2 + x)|
2*|-------------------- + ------------------------------------ + ----------------------|
  |   _________________   /      2         2\                                      3/2 |
  |  /      2        2    \-1 + x *(-2 + x) /*asin(x*(-2 + x))    /     2        2\    |
  \\/  1 - x *(2 - x)                                             \1 - x *(2 - x) /    /
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                                    asin(x*(-2 + x))
2(2x(x−2)(x−1)2(−x2(2−x)2+1)32+2(x−1)2(x2(x−2)2−1)asin⁡(x(x−2))+1−x2(2−x)2+1)asin⁡(x(x−2))\frac{2 \left(\frac{2 x \left(x - 2\right) \left(x - 1\right)^{2}}{\left(- x^{2} \left(2 - x\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{2 \left(x - 1\right)^{2}}{\left(x^{2} \left(x - 2\right)^{2} - 1\right) \operatorname{asin}{\left(x \left(x - 2\right) \right)}} + \frac{1}{\sqrt{- x^{2} \left(2 - x\right)^{2} + 1}}\right)}{\operatorname{asin}{\left(x \left(x - 2\right) \right)}}
Simplify
The third derivative [src] 
           /              2                                                                                             2                    2         2         2                       2                \
           |    2*(-1 + x)                          3                         3*x*(-2 + x)                    4*(-1 + x)                  6*x *(-1 + x) *(-2 + x)            6*x*(-1 + x) *(-2 + x)       |
4*(-1 + x)*|-------------------- + ------------------------------------ + -------------------- + -------------------------------------- + ------------------------ - -------------------------------------|
           |                 3/2   /      2         2\                                     3/2                    3/2                                        5/2                        2                 |
           |/     2        2\      \-1 + x *(-2 + x) /*asin(x*(-2 + x))   /     2        2\      /     2        2\        2                 /     2        2\        /      2         2\                  |
           \\1 - x *(2 - x) /                                             \1 - x *(2 - x) /      \1 - x *(2 - x) /   *asin (x*(-2 + x))     \1 - x *(2 - x) /        \-1 + x *(-2 + x) / *asin(x*(-2 + x))/
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                                                                                              asin(x*(-2 + x))
4(x−1)(6x2(x−2)2(x−1)2(−x2(2−x)2+1)52−6x(x−2)(x−1)2(x2(x−2)2−1)2asin⁡(x(x−2))+3x(x−2)(−x2(2−x)2+1)32+2(x−1)2(−x2(2−x)2+1)32+4(x−1)2(−x2(2−x)2+1)32asin⁡2(x(x−2))+3(x2(x−2)2−1)asin⁡(x(x−2)))asin⁡(x(x−2))\frac{4 \left(x - 1\right) \left(\frac{6 x^{2} \left(x - 2\right)^{2} \left(x - 1\right)^{2}}{\left(- x^{2} \left(2 - x\right)^{2} + 1\right)^{\frac{5}{2}}} - \frac{6 x \left(x - 2\right) \left(x - 1\right)^{2}}{\left(x^{2} \left(x - 2\right)^{2} - 1\right)^{2} \operatorname{asin}{\left(x \left(x - 2\right) \right)}} + \frac{3 x \left(x - 2\right)}{\left(- x^{2} \left(2 - x\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{2 \left(x - 1\right)^{2}}{\left(- x^{2} \left(2 - x\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{4 \left(x - 1\right)^{2}}{\left(- x^{2} \left(2 - x\right)^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \left(x - 2\right) \right)}} + \frac{3}{\left(x^{2} \left(x - 2\right)^{2} - 1\right) \operatorname{asin}{\left(x \left(x - 2\right) \right)}}\right)}{\operatorname{asin}{\left(x \left(x - 2\right) \right)}}
Simplify
The graph
Derivative of ln(arcsin(2x-(x^2)))
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