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How to use it?
- Derivative of:
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Derivative of u
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Derivative of e^x/x^2
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Derivative of cos(x)/x^2
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Derivative of cos(sqrt(x))
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Identical expressions
- ln(arcsin(two x-(x^2)))
- ln(arc sinus of (2x minus (x squared )))
- ln(arc sinus of (two x minus (x squared )))
- ln(arcsin(2x-(x2)))
- lnarcsin2x-x2
- ln(arcsin(2x-(x²)))
- ln(arcsin(2x-(x to the power of 2)))
- lnarcsin2x-x^2
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Similar expressions
- ln(arcsin(2x+(x^2)))
Derivative of ln(arcsin(2x-(x^2)))
The solution
You have entered
[src]
/ / 2\\ log\asin\2*x - x //
$$\log{\left(\operatorname{asin}{\left(- x^{2} + 2 x \right)} \right)}$$
The first derivative
[src]
2 - 2*x
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_________________
/ 2
/ / 2\ / 2\
\/ 1 - \2*x - x / *asin\2*x - x /
$$\frac{2 - 2 x}{\sqrt{1 - \left(- x^{2} + 2 x\right)^{2}} \operatorname{asin}{\left(- x^{2} + 2 x \right)}}$$
The second derivative
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/ 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))
$$\frac{2 \left(\frac{2 x \left(x - 2\right) \left(x - 1\right)^{2}}{\left(- x^{2} \left(2 - x\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{2 \left(x - 1\right)^{2}}{\left(x^{2} \left(x - 2\right)^{2} - 1\right) \operatorname{asin}{\left(x \left(x - 2\right) \right)}} + \frac{1}{\sqrt{- x^{2} \left(2 - x\right)^{2} + 1}}\right)}{\operatorname{asin}{\left(x \left(x - 2\right) \right)}}$$
The third derivative
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/ 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))
$$\frac{4 \left(x - 1\right) \left(\frac{6 x^{2} \left(x - 2\right)^{2} \left(x - 1\right)^{2}}{\left(- x^{2} \left(2 - x\right)^{2} + 1\right)^{\frac{5}{2}}} - \frac{6 x \left(x - 2\right) \left(x - 1\right)^{2}}{\left(x^{2} \left(x - 2\right)^{2} - 1\right)^{2} \operatorname{asin}{\left(x \left(x - 2\right) \right)}} + \frac{3 x \left(x - 2\right)}{\left(- x^{2} \left(2 - x\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{2 \left(x - 1\right)^{2}}{\left(- x^{2} \left(2 - x\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{4 \left(x - 1\right)^{2}}{\left(- x^{2} \left(2 - x\right)^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \left(x - 2\right) \right)}} + \frac{3}{\left(x^{2} \left(x - 2\right)^{2} - 1\right) \operatorname{asin}{\left(x \left(x - 2\right) \right)}}\right)}{\operatorname{asin}{\left(x \left(x - 2\right) \right)}}$$
The graph