Производная log(3,(x^2)+14*x+130)+3
Решение
График
Первая производная
[src]
/ d / log(3) \\|
(14 + 2*x)*|-----|---------||| 2
\dxi_2\log(xi_2)//|xi_2=x + 14*x + 130
$$\left(2 x + 14\right) \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=x^{2} + 14 x + 130 }}$$
Вторая производная
[src]
/ 2 / 2 \ \ |2*(7 + x) *|1 + --------------------|*log(3) | | | / 2 \| | | \ log\130 + x + 14*x// / d / log(3) \\| | 2*|-------------------------------------------- + |-----|---------||| 2 | | 2 \dxi_2\log(xi_2)//|xi_2=x + 14*x + 130| | / 2 \ 2/ 2 \ | \ \130 + x + 14*x/ *log \130 + x + 14*x/ /
$$2 \left(\frac{2 \left(1 + \frac{2}{\log{\left (x^{2} + 14 x + 130 \right )}}\right) \left(x + 7\right)^{2} \log{\left (3 \right )}}{\left(x^{2} + 14 x + 130\right)^{2} \log^{2}{\left (x^{2} + 14 x + 130 \right )}} + \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=x^{2} + 14 x + 130 }}\right)$$
Третья производная
[src]
/ 2 / 2 \ 2 / 2 \ \
| 4*(7 + x) *|1 + --------------------| 4*(7 + x) *|1 + --------------------| |
| 2 | / 2 \| | / 2 \| |
| 6 4*(7 + x) \ log\130 + x + 14*x// \ log\130 + x + 14*x// |
4*(7 + x)*|3 + -------------------- - --------------------------------------- - ------------------------------------- - --------------------------------------|*log(3)
| / 2 \ / 2 \ 2/ 2 \ 2 / 2 \ / 2 \|
\ log\130 + x + 14*x/ \130 + x + 14*x/*log \130 + x + 14*x/ 130 + x + 14*x \130 + x + 14*x/*log\130 + x + 14*x//
----------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2 \ 2/ 2 \
\130 + x + 14*x/ *log \130 + x + 14*x/
$$\frac{4 \log{\left (3 \right )}}{\left(x^{2} + 14 x + 130\right)^{2} \log^{2}{\left (x^{2} + 14 x + 130 \right )}} \left(x + 7\right) \left(- \frac{4 \left(x + 7\right)^{2}}{x^{2} + 14 x + 130} \left(1 + \frac{2}{\log{\left (x^{2} + 14 x + 130 \right )}}\right) - \frac{4 \left(1 + \frac{2}{\log{\left (x^{2} + 14 x + 130 \right )}}\right) \left(x + 7\right)^{2}}{\left(x^{2} + 14 x + 130\right) \log{\left (x^{2} + 14 x + 130 \right )}} - \frac{4 \left(x + 7\right)^{2}}{\left(x^{2} + 14 x + 130\right) \log^{2}{\left (x^{2} + 14 x + 130 \right )}} + 3 + \frac{6}{\log{\left (x^{2} + 14 x + 130 \right )}}\right)$$