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 tanh(x)
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Derivative of (x^5+1)
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Derivative of tanx
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Derivative of tg2x
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Identical expressions
- atan(sqrt(x^ two - one)-ln/sqrt(x^ two - one))
- arc tangent of gent of ( square root of (x squared minus 1) minus ln divide by square root of (x squared minus 1))
- arc tangent of gent of ( square root of (x to the power of two minus one) minus ln divide by square root of (x to the power of two minus one))
- atan(√(x^2-1)-ln/√(x^2-1))
- atan(sqrt(x2-1)-ln/sqrt(x2-1))
- atansqrtx2-1-ln/sqrtx2-1
- atan(sqrt(x²-1)-ln/sqrt(x²-1))
- atan(sqrt(x to the power of 2-1)-ln/sqrt(x to the power of 2-1))
- atansqrtx^2-1-ln/sqrtx^2-1
- atan(sqrt(x^2-1)-ln divide by sqrt(x^2-1))
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Similar expressions
- atan(sqrt(x^2-1)-ln/sqrt(x^2+1))
- atan(sqrt(x^2+1)-ln/sqrt(x^2-1))
- atan(sqrt(x^2-1)+ln/sqrt(x^2-1))
- arctan(sqrt(x^2-1)-ln/sqrt(x^2-1))
Derivative of atan(sqrt(x^2-1)-ln/sqrt(x^2-1))
The solution
You have entered
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/ ________ \
| / 2 log(x) |
atan|\/ x - 1 - -----------|
| ________|
| / 2 |
\ \/ x - 1 /
$$\operatorname{atan}{\left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}} \right)}$$
atan(sqrt(x^2 - 1) - log(x)/sqrt(x^2 - 1))
The first derivative
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x 1 x*log(x)
----------- - ------------- + -----------
________ ________ 3/2
/ 2 / 2 / 2 \
\/ x - 1 x*\/ x - 1 \x - 1/
-----------------------------------------
2
/ ________ \
| / 2 log(x) |
1 + |\/ x - 1 - -----------|
| ________|
| / 2 |
\ \/ x - 1 /
$$\frac{\frac{x}{\sqrt{x^{2} - 1}} + \frac{x \log{\left(x \right)}}{\left(x^{2} - 1\right)^{\frac{3}{2}}} - \frac{1}{x \sqrt{x^{2} - 1}}}{\left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}}\right)^{2} + 1}$$
The second derivative
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2 2 2 / _________ \
1 2 log(x) x 3*x *log(x) / 1 x*log(x)\ | / 2 log(x) |
1 + -- + ------- + ------- - ------- - ----------- 2*|x - - + --------| *|\/ -1 + x - ------------|
2 2 2 2 2 | x 2 | | _________|
x -1 + x -1 + x -1 + x / 2\ \ -1 + x / | / 2 |
\-1 + x / \ \/ -1 + x /
-------------------------------------------------- - ---------------------------------------------------
_________ / 2\
/ 2 | / _________ \ |
\/ -1 + x | | / 2 log(x) | | / 2\
|1 + |\/ -1 + x - ------------| |*\-1 + x /
| | _________| |
| | / 2 | |
\ \ \/ -1 + x / /
--------------------------------------------------------------------------------------------------------
2
/ _________ \
| / 2 log(x) |
1 + |\/ -1 + x - ------------|
| _________|
| / 2 |
\ \/ -1 + x /
$$\frac{- \frac{2 \left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}}\right) \left(x + \frac{x \log{\left(x \right)}}{x^{2} - 1} - \frac{1}{x}\right)^{2}}{\left(x^{2} - 1\right) \left(\left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}}\right)^{2} + 1\right)} + \frac{- \frac{x^{2}}{x^{2} - 1} - \frac{3 x^{2} \log{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + 1 + \frac{\log{\left(x \right)}}{x^{2} - 1} + \frac{2}{x^{2} - 1} + \frac{1}{x^{2}}}{\sqrt{x^{2} - 1}}}{\left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}}\right)^{2} + 1}$$
The third derivative
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2
3 3 / _________ \ 3 / _________ \ / 2 2 \
2 3*x 3*x 9*x 15*x *log(x) 9*x*log(x) 3 | / 2 log(x) | / 1 x*log(x)\ | / 2 log(x) | / 1 x*log(x)\ | 1 2 log(x) x 3*x *log(x)|
-- - ---------- + ------- + ---------- - ------------ + ---------- / 1 x*log(x)\ 8*|\/ -1 + x - ------------| *|x - - + --------| 6*|\/ -1 + x - ------------|*|x - - + --------|*|1 + -- + ------- + ------- - ------- - -----------|
3 2 2 2 3 2 2*|x - - + --------| | _________| | x 2 | | _________| | x 2 | | 2 2 2 2 2|
x / 2\ -1 + x / 2\ / 2\ / 2\ | x 2 | | / 2 | \ -1 + x / | / 2 | \ -1 + x / | x -1 + x -1 + x -1 + x / 2\ |
\-1 + x / \-1 + x / \-1 + x / \-1 + x / \ -1 + x / \ \/ -1 + x / \ \/ -1 + x / \ \-1 + x / /
- ------------------------------------------------------------------ - ------------------------------------------------- + ---------------------------------------------------- - -------------------------------------------------------------------------------------------------------
_________ / 2\ 2 / 2\
/ 2 | / _________ \ | 3/2 / 2\ | / _________ \ |
\/ -1 + x | | / 2 log(x) | | / 2\ | / _________ \ | 3/2 | | / 2 log(x) | | / 2\
|1 + |\/ -1 + x - ------------| |*\-1 + x / | | / 2 log(x) | | / 2\ |1 + |\/ -1 + x - ------------| |*\-1 + x /
| | _________| | |1 + |\/ -1 + x - ------------| | *\-1 + x / | | _________| |
| | / 2 | | | | _________| | | | / 2 | |
\ \ \/ -1 + x / / | | / 2 | | \ \ \/ -1 + x / /
\ \ \/ -1 + x / /
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2
/ _________ \
| / 2 log(x) |
1 + |\/ -1 + x - ------------|
| _________|
| / 2 |
\ \/ -1 + x /
$$\frac{- \frac{6 \left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}}\right) \left(x + \frac{x \log{\left(x \right)}}{x^{2} - 1} - \frac{1}{x}\right) \left(- \frac{x^{2}}{x^{2} - 1} - \frac{3 x^{2} \log{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + 1 + \frac{\log{\left(x \right)}}{x^{2} - 1} + \frac{2}{x^{2} - 1} + \frac{1}{x^{2}}\right)}{\left(x^{2} - 1\right) \left(\left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}}\right)^{2} + 1\right)} - \frac{- \frac{3 x^{3}}{\left(x^{2} - 1\right)^{2}} - \frac{15 x^{3} \log{\left(x \right)}}{\left(x^{2} - 1\right)^{3}} + \frac{3 x}{x^{2} - 1} + \frac{9 x \log{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{9 x}{\left(x^{2} - 1\right)^{2}} + \frac{2}{x^{3}}}{\sqrt{x^{2} - 1}} + \frac{8 \left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}}\right)^{2} \left(x + \frac{x \log{\left(x \right)}}{x^{2} - 1} - \frac{1}{x}\right)^{3}}{\left(x^{2} - 1\right)^{\frac{3}{2}} \left(\left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}}\right)^{2} + 1\right)^{2}} - \frac{2 \left(x + \frac{x \log{\left(x \right)}}{x^{2} - 1} - \frac{1}{x}\right)^{3}}{\left(x^{2} - 1\right)^{\frac{3}{2}} \left(\left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}}\right)^{2} + 1\right)}}{\left(\sqrt{x^{2} - 1} - \frac{\log{\left(x \right)}}{\sqrt{x^{2} - 1}}\right)^{2} + 1}$$