Подробное решение
-
Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
/ 2\
\x / / x \
(1 + log(x)) *|---------- + 2*x*log(1 + log(x))|
\1 + log(x) /
$$\left(2 x \log{\left(\log{\left(x \right)} + 1 \right)} + \frac{x}{\log{\left(x \right)} + 1}\right) \left(\log{\left(x \right)} + 1\right)^{x^{2}}$$
/ 2\ / 2\
\x / | 1 3 2 / 1 \ |
(1 + log(x)) *|- ------------- + 2*log(1 + log(x)) + ---------- + x *|---------- + 2*log(1 + log(x))| |
| 2 1 + log(x) \1 + log(x) / |
\ (1 + log(x)) /
$$\left(\log{\left(x \right)} + 1\right)^{x^{2}} \left(x^{2} \left(2 \log{\left(\log{\left(x \right)} + 1 \right)} + \frac{1}{\log{\left(x \right)} + 1}\right)^{2} + 2 \log{\left(\log{\left(x \right)} + 1 \right)} + \frac{3}{\log{\left(x \right)} + 1} - \frac{1}{\left(\log{\left(x \right)} + 1\right)^{2}}\right)$$
/ 3 2 \
| 2 - ---------- + ------------- |
/ 2\ | 3 1 + log(x) 2 |
\x / | 3 / 1 \ (1 + log(x)) / 1 \ / 1 3 \|
(1 + log(x)) *|x *|---------- + 2*log(1 + log(x))| + ------------------------------ + 3*x*|---------- + 2*log(1 + log(x))|*|- ------------- + 2*log(1 + log(x)) + ----------||
| \1 + log(x) / x*(1 + log(x)) \1 + log(x) / | 2 1 + log(x)||
\ \ (1 + log(x)) //
$$\left(\log{\left(x \right)} + 1\right)^{x^{2}} \left(x^{3} \left(2 \log{\left(\log{\left(x \right)} + 1 \right)} + \frac{1}{\log{\left(x \right)} + 1}\right)^{3} + 3 x \left(2 \log{\left(\log{\left(x \right)} + 1 \right)} + \frac{1}{\log{\left(x \right)} + 1}\right) \left(2 \log{\left(\log{\left(x \right)} + 1 \right)} + \frac{3}{\log{\left(x \right)} + 1} - \frac{1}{\left(\log{\left(x \right)} + 1\right)^{2}}\right) + \frac{2 - \frac{3}{\log{\left(x \right)} + 1} + \frac{2}{\left(\log{\left(x \right)} + 1\right)^{2}}}{x \left(\log{\left(x \right)} + 1\right)}\right)$$