The first derivative
[src]
x
3*2 x
-------- + 2 *atan(3*x)*log(2)
2
1 + 9*x
$$2^{x} \log{\left(2 \right)} \operatorname{atan}{\left(3 x \right)} + \frac{3 \cdot 2^{x}}{9 x^{2} + 1}$$
The second derivative
[src]
x / 2 54*x 6*log(2)\
2 *|log (2)*atan(3*x) - ----------- + --------|
| 2 2|
| / 2\ 1 + 9*x |
\ \1 + 9*x / /
$$2^{x} \left(- \frac{54 x}{\left(9 x^{2} + 1\right)^{2}} + \log{\left(2 \right)}^{2} \operatorname{atan}{\left(3 x \right)} + \frac{6 \log{\left(2 \right)}}{9 x^{2} + 1}\right)$$
The third derivative
[src]
/ / 2 \ \
| | 36*x | |
| 54*|-1 + --------| |
| 2 | 2| |
x | 3 9*log (2) \ 1 + 9*x / 162*x*log(2)|
2 *|log (2)*atan(3*x) + --------- + ------------------ - ------------|
| 2 2 2 |
| 1 + 9*x / 2\ / 2\ |
\ \1 + 9*x / \1 + 9*x / /
$$2^{x} \left(- \frac{162 x \log{\left(2 \right)}}{\left(9 x^{2} + 1\right)^{2}} + \log{\left(2 \right)}^{3} \operatorname{atan}{\left(3 x \right)} + \frac{9 \log{\left(2 \right)}^{2}}{9 x^{2} + 1} + \frac{54 \cdot \left(\frac{36 x^{2}}{9 x^{2} + 1} - 1\right)}{\left(9 x^{2} + 1\right)^{2}}\right)$$