Mister Exam
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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
- Derivative of log(2)
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Derivative of 1/(x-1)
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Derivative of x*ctgx
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Derivative of sin(lnx)
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Identical expressions
- arcsinx^ two +arccos2x.
- arc sinus of x squared plus arc co sinus of e of 2x.
- arc sinus of x to the power of two plus arc co sinus of e of 2x.
- arcsinx2+arccos2x.
- arcsinx²+arccos2x.
- arcsinx to the power of 2+arccos2x.
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Similar expressions
- arcsinx^2-arccos2x.
Derivative of arcsinx^2+arccos2x.
The solution
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2 asin (x) + acos(2*x)
$$\operatorname{asin}^{2}{\left(x \right)} + \operatorname{acos}{\left(2 x \right)}$$
d / 2 \ --\asin (x) + acos(2*x)/ dx
$$\frac{d}{d x} \left(\operatorname{asin}^{2}{\left(x \right)} + \operatorname{acos}{\left(2 x \right)}\right)$$
The first derivative
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2 2*asin(x)
- ------------- + -----------
__________ ________
/ 2 / 2
\/ 1 - 4*x \/ 1 - x
$$\frac{2 \operatorname{asin}{\left(x \right)}}{\sqrt{- x^{2} + 1}} - \frac{2}{\sqrt{- 4 x^{2} + 1}}$$
The second derivative
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/ 1 4*x x*asin(x) \ 2*|- ------- - ------------- + -----------| | 2 3/2 3/2| | -1 + x / 2\ / 2\ | \ \1 - 4*x / \1 - x / /
$$2 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1} - \frac{4 x}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}}\right)$$
The third derivative
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/ 2 2 \ | 4 asin(x) 48*x 3*x 3*x *asin(x)| 2*|- ------------- + ----------- - ------------- + ---------- + ------------| | 3/2 3/2 5/2 2 5/2 | | / 2\ / 2\ / 2\ / 2\ / 2\ | \ \1 - 4*x / \1 - x / \1 - 4*x / \-1 + x / \1 - x / /
$$2 \cdot \left(\frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{48 x^{2}}{\left(- 4 x^{2} + 1\right)^{\frac{5}{2}}} - \frac{4}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}}\right)$$
The graph