The first derivative
[src]
x
e
-----------------
/ 2\
| / x \ |
| \e - 3/ |
4*|1 + ---------|
\ 4 /
$$\frac{e^{x}}{4 \left(\frac{\left(e^{x} - 3\right)^{2}}{4} + 1\right)}$$
The second derivative
[src]
/ / x\ x\
| 2*\-3 + e /*e | x
|1 - --------------|*e
| 2|
| / x\ |
\ 4 + \-3 + e / /
-----------------------
2
/ x\
4 + \-3 + e /
$$\frac{\left(1 - \frac{2 \left(e^{x} - 3\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4}\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4}$$
The third derivative
[src]
/ 2 \
| 2*x / x\ x / x\ 2*x|
| 2*e 6*\-3 + e /*e 8*\-3 + e / *e | x
|1 - -------------- - -------------- + -----------------|*e
| 2 2 2|
| / x\ / x\ / 2\ |
| 4 + \-3 + e / 4 + \-3 + e / | / x\ | |
\ \4 + \-3 + e / / /
------------------------------------------------------------
2
/ x\
4 + \-3 + e /
$$\frac{\left(1 - \frac{6 \left(e^{x} - 3\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4} - \frac{2 e^{2 x}}{\left(e^{x} - 3\right)^{2} + 4} + \frac{8 \left(e^{x} - 3\right)^{2} e^{2 x}}{\left(\left(e^{x} - 3\right)^{2} + 4\right)^{2}}\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4}$$