Производная log((1/2),sqrt(2)/(3*x+1))
Решение
Вы ввели
[TeX]
[pretty]
[text]
/ ___ \ | \/ 2 | log|1/2, -------| \ 3*x + 1/
$$\log{\left (\frac{1}{2},\frac{\sqrt{2}}{3 x + 1} \right )}$$
График
Первая производная
[TeX]
[pretty]
[text]
___ / d / -log(2) \\| ___
-3*\/ 2 *|-----|---------||| \/ 2
\dxi_2\log(xi_2)//|xi_2=-------
3*x + 1
----------------------------------------
2
(3*x + 1)
$$- \frac{3 \sqrt{2}}{\left(3 x + 1\right)^{2}} \left. \frac{d}{d \xi_{2}}\left(- \frac{\log{\left (2 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=\frac{\sqrt{2}}{3 x + 1} }}$$
Вторая производная
[TeX]
[pretty]
[text]
/ / 2 \ \
| |1 + ------------|*log(2) |
| | / ___ \| ___ / d / -log(2) \\| ___ |
| | | \/ 2 || 2*\/ 2 *|-----|---------||| \/ 2 |
| | log|-------|| \dxi_2\log(xi_2)//|xi_2=-------|
| \ \1 + 3*x// 3*x + 1|
9*|- ------------------------- + ---------------------------------------|
| / ___ \ 1 + 3*x |
| 2| \/ 2 | |
| log |-------| |
\ \1 + 3*x/ /
-------------------------------------------------------------------------
2
(1 + 3*x)
$$\frac{1}{\left(3 x + 1\right)^{2}} \left(- \frac{9 \left(1 + \frac{2}{\log{\left (\frac{\sqrt{2}}{3 x + 1} \right )}}\right) \log{\left (2 \right )}}{\log^{2}{\left (\frac{\sqrt{2}}{3 x + 1} \right )}} + \frac{18 \sqrt{2}}{3 x + 1} \left. \frac{d}{d \xi_{2}}\left(- \frac{\log{\left (2 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=\frac{\sqrt{2}}{3 x + 1} }}\right)$$
Третья производная
[TeX]
[pretty]
[text]
/ / 2 \ / 2 \ \
| |1 + ------------|*log(2) 2*|1 + ------------|*log(2)|
| | / ___ \| ___ / d / -log(2) \\| ___ | / ___ \| |
| | | \/ 2 || 3*\/ 2 *|-----|---------||| \/ 2 | | \/ 2 || |
| | log|-------|| \dxi_2\log(xi_2)//|xi_2=------- | log|-------|| |
| log(2) \ \1 + 3*x// 3*x + 1 \ \1 + 3*x// |
54*|- ------------- - ------------------------- - --------------------------------------- + ---------------------------|
| / ___ \ / ___ \ 1 + 3*x / ___ \ |
| 4| \/ 2 | 3| \/ 2 | 2| \/ 2 | |
| log |-------| log |-------| log |-------| |
\ \1 + 3*x/ \1 + 3*x/ \1 + 3*x/ /
------------------------------------------------------------------------------------------------------------------------
3
(1 + 3*x)
$$\frac{1}{\left(3 x + 1\right)^{3}} \left(\frac{108 \left(1 + \frac{2}{\log{\left (\frac{\sqrt{2}}{3 x + 1} \right )}}\right) \log{\left (2 \right )}}{\log^{2}{\left (\frac{\sqrt{2}}{3 x + 1} \right )}} - \frac{54 \left(1 + \frac{2}{\log{\left (\frac{\sqrt{2}}{3 x + 1} \right )}}\right) \log{\left (2 \right )}}{\log^{3}{\left (\frac{\sqrt{2}}{3 x + 1} \right )}} - \frac{54 \log{\left (2 \right )}}{\log^{4}{\left (\frac{\sqrt{2}}{3 x + 1} \right )}} - \frac{162 \sqrt{2}}{3 x + 1} \left. \frac{d}{d \xi_{2}}\left(- \frac{\log{\left (2 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=\frac{\sqrt{2}}{3 x + 1} }}\right)$$