Производная (x-1)^(2/x)

Вы ввели

       2
       -
       x
(x - 1) 

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

       2                             
       -                             
       x /  2*log(x - 1)       2    \
(x - 1) *|- ------------ + ---------|
         |        2        x*(x - 1)|
         \       x                  /

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

Вторая производная

            /                                                   2                \
          2 |                             /  1      log(-1 + x)\                 |
          - |                           2*|------ - -----------|                 |
          x |      1           2          \-1 + x        x     /    2*log(-1 + x)|
2*(-1 + x) *|- --------- - ---------- + ------------------------- + -------------|
            |          2   x*(-1 + x)               x                      2     |
            \  (-1 + x)                                                   x      /
----------------------------------------------------------------------------------
                                        x                                         

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

Третья производная

            /                                                                  3                   /  1      log(-1 + x)\ /    1       2*log(-1 + x)       2     \\
          2 |                                            /  1      log(-1 + x)\                  6*|------ - -----------|*|--------- - ------------- + ----------||
          - |                                          4*|------ - -----------|                    \-1 + x        x     / |        2          2        x*(-1 + x)||
          x |    2       6*log(-1 + x)        3          \-1 + x        x     /         6                                 \(-1 + x)          x                   /|
2*(-1 + x) *|--------- - ------------- + ----------- + ------------------------- + ----------- - -----------------------------------------------------------------|
            |        3          3                  2                2               2                                            x                                |
            \(-1 + x)          x         x*(-1 + x)                x               x *(-1 + x)                                                                    /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                 x                                                                                 

$$\frac{2}{x} \left(x - 1\right)^{\frac{2}{x}} \left(\frac{2}{\left(x - 1\right)^{3}} - \frac{6}{x} \left(\frac{1}{x - 1} - \frac{1}{x} \log{\left (x - 1 \right )}\right) \left(\frac{1}{\left(x - 1\right)^{2}} + \frac{2}{x \left(x - 1\right)} - \frac{2}{x^{2}} \log{\left (x - 1 \right )}\right) + \frac{3}{x \left(x - 1\right)^{2}} + \frac{4}{x^{2}} \left(\frac{1}{x - 1} - \frac{1}{x} \log{\left (x - 1 \right )}\right)^{3} + \frac{6}{x^{2} \left(x - 1\right)} - \frac{6}{x^{3}} \log{\left (x - 1 \right )}\right)$$