Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of x-x^2
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Derivative of x^3/(x+1)^2
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Derivative of x^2*e^(3*x)
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Derivative of x^2-4x+3
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Identical expressions
- lnarcsin2x
- lnarc sinus of 2x
Derivative of lnarcsin2x
The solution
You have entered
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log(asin(2*x))
$$\log{\left(\operatorname{asin}{\left(2 x \right)} \right)}$$
log(asin(2*x))
The first derivative
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2 ----------------------- __________ / 2 \/ 1 - 4*x *asin(2*x)
$$\frac{2}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}$$
The second derivative
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/ 1 2*x \
4*|--------------------- + -------------|
|/ 2\ 3/2|
|\-1 + 4*x /*asin(2*x) / 2\ |
\ \1 - 4*x / /
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asin(2*x)
$$\frac{4 \left(\frac{2 x}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\left(4 x^{2} - 1\right) \operatorname{asin}{\left(2 x \right)}}\right)}{\operatorname{asin}{\left(2 x \right)}}$$
The third derivative
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/ 2 \
| 1 2 12*x 6*x |
8*|------------- + ------------------------ + ------------- - ----------------------|
| 3/2 3/2 5/2 2 |
|/ 2\ / 2\ 2 / 2\ / 2\ |
\\1 - 4*x / \1 - 4*x / *asin (2*x) \1 - 4*x / \-1 + 4*x / *asin(2*x)/
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asin(2*x)
$$\frac{8 \left(\frac{12 x^{2}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} - \frac{6 x}{\left(4 x^{2} - 1\right)^{2} \operatorname{asin}{\left(2 x \right)}} + \frac{1}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(2 x \right)}}\right)}{\operatorname{asin}{\left(2 x \right)}}$$
The graph