Производная (x+2)^(log(x))

Вы ввели

       log(x)
(x + 2)      

$$\left(x + 2\right)^{\log{\left (x \right )}}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

   $\left(\log{\left (\log{\left (x \right )} \right )} + 1\right) \log^{\log{\left (x \right )}}{\left (x \right )}$

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Ответ:

$\left(\log{\left (\log{\left (x \right )} \right )} + 1\right) \log^{\log{\left (x \right )}}{\left (x \right )}$

Первая производная

       log(x) /log(x + 2)   log(x)\
(x + 2)      *|---------- + ------|
              \    x        x + 2 /

$$\left(x + 2\right)^{\log{\left (x \right )}} \left(\frac{\log{\left (x \right )}}{x + 2} + \frac{1}{x} \log{\left (x + 2 \right )}\right)$$

Вторая производная

              /                     2                                    \
       log(x) |/log(2 + x)   log(x)\    log(2 + x)    log(x)        2    |
(2 + x)      *||---------- + ------|  - ---------- - -------- + ---------|
              |\    x        2 + x /         2              2   x*(2 + x)|
              \                             x        (2 + x)             /

$$\left(x + 2\right)^{\log{\left (x \right )}} \left(\left(\frac{\log{\left (x \right )}}{x + 2} + \frac{1}{x} \log{\left (x + 2 \right )}\right)^{2} - \frac{\log{\left (x \right )}}{\left(x + 2\right)^{2}} + \frac{2}{x \left(x + 2\right)} - \frac{1}{x^{2}} \log{\left (x + 2 \right )}\right)$$

Третья производная

              /                     3                                                                                                                  \
       log(x) |/log(2 + x)   log(x)\        3            3          /log(2 + x)   log(x)\ /log(2 + x)    log(x)        2    \   2*log(2 + x)   2*log(x)|
(2 + x)      *||---------- + ------|  - ---------- - ---------- - 3*|---------- + ------|*|---------- + -------- - ---------| + ------------ + --------|
              |\    x        2 + x /             2    2             \    x        2 + x / |     2              2   x*(2 + x)|         3               3|
              \                         x*(2 + x)    x *(2 + x)                           \    x        (2 + x)             /        x         (2 + x) /

$$\left(x + 2\right)^{\log{\left (x \right )}} \left(\left(\frac{\log{\left (x \right )}}{x + 2} + \frac{1}{x} \log{\left (x + 2 \right )}\right)^{3} - 3 \left(\frac{\log{\left (x \right )}}{x + 2} + \frac{1}{x} \log{\left (x + 2 \right )}\right) \left(\frac{\log{\left (x \right )}}{\left(x + 2\right)^{2}} - \frac{2}{x \left(x + 2\right)} + \frac{1}{x^{2}} \log{\left (x + 2 \right )}\right) + \frac{2 \log{\left (x \right )}}{\left(x + 2\right)^{3}} - \frac{3}{x \left(x + 2\right)^{2}} - \frac{3}{x^{2} \left(x + 2\right)} + \frac{2}{x^{3}} \log{\left (x + 2 \right )}\right)$$