Производная (x+2)^(2+log(x))

Вы ввели

       2 + log(x)
(x + 2)          

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

$$\left(x + 2\right)^{\log{\left (x \right )} + 2} \left(\left(\frac{\log{\left (x \right )} + 2}{x + 2} + \frac{1}{x} \log{\left (x + 2 \right )}\right)^{3} - 3 \left(\frac{\log{\left (x \right )} + 2}{x + 2} + \frac{1}{x} \log{\left (x + 2 \right )}\right) \left(\frac{\log{\left (x \right )} + 2}{\left(x + 2\right)^{2}} - \frac{2}{x \left(x + 2\right)} + \frac{1}{x^{2}} \log{\left (x + 2 \right )}\right) + \frac{1}{\left(x + 2\right)^{3}} \left(2 \log{\left (x \right )} + 4\right) - \frac{3}{x \left(x + 2\right)^{2}} - \frac{3}{x^{2} \left(x + 2\right)} + \frac{2}{x^{3}} \log{\left (x + 2 \right )}\right)$$