Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of sin(2*x^2+3)
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Derivative of f(x)=5
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Derivative of x+ln(x^2-4)
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Derivative of x-8
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Identical expressions
- (asin(2x)^ three)
- ( arc sinus of e of (2x) cubed )
- ( arc sinus of e of (2x) to the power of three)
- (asin(2x)3)
- asin2x3
- (asin(2x)³)
- (asin(2x) to the power of 3)
- asin2x^3
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Similar expressions
- (arcsin(2x)^3)
Derivative of (asin(2x)^3)
The solution
The first derivative
[src]
2 6*asin (2*x) ------------- __________ / 2 \/ 1 - 4*x
$$\frac{6 \operatorname{asin}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}$$
The second derivative
[src]
/ 1 x*asin(2*x) \ 24*|- --------- + -------------|*asin(2*x) | 2 3/2| | -1 + 4*x / 2\ | \ \1 - 4*x / /
$$24 \left(\frac{x \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{4 x^{2} - 1}\right) \operatorname{asin}{\left(2 x \right)}$$
The third derivative
[src]
/ 2 2 2 \ | 2 asin (2*x) 12*x*asin(2*x) 12*x *asin (2*x)| 24*|------------- + ------------- + -------------- + ----------------| | 3/2 3/2 2 5/2 | |/ 2\ / 2\ / 2\ / 2\ | \\1 - 4*x / \1 - 4*x / \-1 + 4*x / \1 - 4*x / /
$$24 \left(\frac{12 x^{2} \operatorname{asin}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} + \frac{12 x \operatorname{asin}{\left(2 x \right)}}{\left(4 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right)$$