The first derivative
[src]
1 t
---------- - -----------------
/ 2\ ______________
| x | / 2
2*|1 + --| \/ 1 - (1 - x)
\ 4 /
$$- \frac{t}{\sqrt{1 - \left(1 - x\right)^{2}}} + \frac{1}{2 \left(\frac{x^{2}}{4} + 1\right)}$$
The second derivative
[src]
/ 4*x t*(-1 + x) \
-|--------- + -----------------|
| 2 3/2|
|/ 2\ / 2\ |
\\4 + x / \1 - (1 - x) / /
$$- (\frac{t \left(x - 1\right)}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{3}{2}}} + \frac{4 x}{\left(x^{2} + 4\right)^{2}})$$
The third derivative
[src]
2 2
4 t 16*x 3*t*(-1 + x)
- --------- - ----------------- + --------- - -----------------
2 3/2 3 5/2
/ 2\ / 2\ / 2\ / 2\
\4 + x / \1 - (1 - x) / \4 + x / \1 - (1 - x) /
$$- \frac{t}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{3}{2}}} - \frac{3 t \left(x - 1\right)^{2}}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{5}{2}}} + \frac{16 x^{2}}{\left(x^{2} + 4\right)^{3}} - \frac{4}{\left(x^{2} + 4\right)^{2}}$$