Mister Exam
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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of x^2*sin(2*x-3)
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Derivative of (x+1)^2*(x-5)-6
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Derivative of log(11*x)
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Derivative of log(t-1)
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Identical expressions
- tg(two arccossqrt(one -2x^2))
- tg(2arc co sinus of e of square root of (1 minus 2x squared ))
- tg(two arc co sinus of e of square root of (one minus 2x squared ))
- tg(2arccos√(1-2x^2))
- tg(2arccossqrt(1-2x2))
- tg2arccossqrt1-2x2
- tg(2arccossqrt(1-2x²))
- tg(2arccossqrt(1-2x to the power of 2))
- tg2arccossqrt1-2x^2
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Similar expressions
- tg(2arccossqrt(1+2x^2))
Derivative of tg(2arccossqrt(1-2x^2))
The solution
You have entered
[src]
/ / __________\\ | | / 2 || tan\2*acos\\/ 1 - 2*x //
$$\tan{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)}$$
/ / / __________\\\ d | | | / 2 ||| --\tan\2*acos\\/ 1 - 2*x /// dx
$$\frac{d}{d x} \tan{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)}$$
The first derivative
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/ / / __________\\\
___ | 2| | / 2 |||
2*x*\/ 2 *\1 + tan \2*acos\\/ 1 - 2*x ///
-------------------------------------------
__________
/ 2
\/ 1 - 2*x *|x|
$$\frac{2 \sqrt{2} x \left(\tan^{2}{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)} + 1\right)}{\sqrt{- 2 x^{2} + 1} \left|{x}\right|}$$
The second derivative
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/ / / __________\\ \
/ / / __________\\\ | | | / 2 || ___ ___ ___ 2 |
| 2| | / 2 ||| | 8*tan\2*acos\\/ 1 - 2*x // \/ 2 \/ 2 *sign(x) 2*\/ 2 *x |
2*\1 + tan \2*acos\\/ 1 - 2*x ///*|- ---------------------------- + ----------------- - --------------- + -----------------|
| 2 __________ __________ 3/2 |
| -1 + 2*x / 2 / 2 / 2\ |
\ \/ 1 - 2*x *|x| x*\/ 1 - 2*x \1 - 2*x / *|x|/
$$2 \left(\tan^{2}{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)} + 1\right) \left(- \frac{8 \tan{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)}}{2 x^{2} - 1} - \frac{\sqrt{2} \operatorname{sign}{\left(x \right)}}{x \sqrt{- 2 x^{2} + 1}} + \frac{2 \sqrt{2} x^{2}}{\left(- 2 x^{2} + 1\right)^{\frac{3}{2}} \left|{x}\right|} + \frac{\sqrt{2}}{\sqrt{- 2 x^{2} + 1} \left|{x}\right|}\right)$$
The third derivative
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/ / / __________\\ / / __________\\ / / __________\\ / / / __________\\\ / / __________\\\
/ / / __________\\\ | | | / 2 || ___ | | / 2 || ___ ___ | | / 2 || ___ 3 ___ | 2| | / 2 ||| ___ 2| | / 2 |||
| 2| | / 2 ||| | 4*tan\2*acos\\/ 1 - 2*x // 2*\/ 2 *sign(x) 24*x*tan\2*acos\\/ 1 - 2*x // \/ 2 *DiracDelta(x) 3*x*\/ 2 4*sign(x)*tan\2*acos\\/ 1 - 2*x // 6*\/ 2 *x 8*x*\/ 2 *\1 + tan \2*acos\\/ 1 - 2*x /// 16*x*\/ 2 *tan \2*acos\\/ 1 - 2*x //|
4*\1 + tan \2*acos\\/ 1 - 2*x ///*|- ---------------------------- - --------------- + ------------------------------- - ------------------- + ----------------- + ------------------------------------ + ----------------- + ------------------------------------------- + --------------------------------------|
| / 2\ 3/2 2 __________ 3/2 / 2\ 5/2 3/2 3/2 |
| x*\-1 + 2*x / / 2\ / 2\ / 2 / 2\ \-1 + 2*x /*|x| / 2\ / 2\ / 2\ |
\ \1 - 2*x / \-1 + 2*x / x*\/ 1 - 2*x \1 - 2*x / *|x| \1 - 2*x / *|x| \1 - 2*x / *|x| \1 - 2*x / *|x| /
$$4 \left(\tan^{2}{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)} + 1\right) \left(\frac{24 x \tan{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)}}{\left(2 x^{2} - 1\right)^{2}} + \frac{4 \tan{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)} \operatorname{sign}{\left(x \right)}}{\left(2 x^{2} - 1\right) \left|{x}\right|} + \frac{16 \sqrt{2} x \tan^{2}{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)}}{\left(- 2 x^{2} + 1\right)^{\frac{3}{2}} \left|{x}\right|} - \frac{4 \tan{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)}}{x \left(2 x^{2} - 1\right)} - \frac{\sqrt{2} \delta\left(x\right)}{x \sqrt{- 2 x^{2} + 1}} + \frac{8 \sqrt{2} x \left(\tan^{2}{\left(2 \operatorname{acos}{\left(\sqrt{- 2 x^{2} + 1} \right)} \right)} + 1\right)}{\left(- 2 x^{2} + 1\right)^{\frac{3}{2}} \left|{x}\right|} - \frac{2 \sqrt{2} \operatorname{sign}{\left(x \right)}}{\left(- 2 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6 \sqrt{2} x^{3}}{\left(- 2 x^{2} + 1\right)^{\frac{5}{2}} \left|{x}\right|} + \frac{3 \sqrt{2} x}{\left(- 2 x^{2} + 1\right)^{\frac{3}{2}} \left|{x}\right|}\right)$$
The graph