The first derivative
[src]
___
-\/ 2
----------------------
_____________
/ 2
/ log (x)
2*x* / 1 - -------
\/ 2
$$- \frac{\sqrt{2}}{2 x \sqrt{- \frac{\log{\left(x \right)}^{2}}{2} + 1}}$$
The second derivative
[src]
___ / log(x) \
\/ 2 *|2 - -----------|
| 2 |
| log (x)|
| 1 - -------|
\ 2 /
-----------------------
_____________
/ 2
2 / log (x)
4*x * / 1 - -------
\/ 2
$$\frac{\sqrt{2} \cdot \left(2 - \frac{\log{\left(x \right)}}{- \frac{\log{\left(x \right)}^{2}}{2} + 1}\right)}{4 x^{2} \sqrt{- \frac{\log{\left(x \right)}^{2}}{2} + 1}}$$
The third derivative
[src]
/ 2 \
___ | 1 3*log (x) 3*log(x) |
\/ 2 *|-1 - --------------- - ---------------- + ---------------|
| / 2 \ 2 / 2 \|
| | log (x)| / 2 \ | log (x)||
| 4*|1 - -------| | log (x)| 4*|1 - -------||
| \ 2 / 8*|1 - -------| \ 2 /|
\ \ 2 / /
-----------------------------------------------------------------
_____________
/ 2
3 / log (x)
x * / 1 - -------
\/ 2
$$\frac{\sqrt{2} \left(-1 + \frac{3 \log{\left(x \right)}}{4 \cdot \left(- \frac{\log{\left(x \right)}^{2}}{2} + 1\right)} - \frac{3 \log{\left(x \right)}^{2}}{8 \left(- \frac{\log{\left(x \right)}^{2}}{2} + 1\right)^{2}} - \frac{1}{4 \cdot \left(- \frac{\log{\left(x \right)}^{2}}{2} + 1\right)}\right)}{x^{3} \sqrt{- \frac{\log{\left(x \right)}^{2}}{2} + 1}}$$