Производная (x+5)^acos(x)

Вы ввели

       acos(x)
(x + 5)       

$$\left(x + 5\right)^{\operatorname{acos}{\left (x \right )}}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

       acos(x) /acos(x)    log(x + 5)\
(x + 5)       *|------- - -----------|
               | x + 5       ________|
               |            /      2 |
               \          \/  1 - x  /

$$\left(x + 5\right)^{\operatorname{acos}{\left (x \right )}} \left(- \frac{\log{\left (x + 5 \right )}}{\sqrt{- x^{2} + 1}} + \frac{\operatorname{acos}{\left (x \right )}}{x + 5}\right)$$

Вторая производная

               /                       2                                                \
       acos(x) |/ log(5 + x)   acos(x)\    acos(x)             2            x*log(5 + x)|
(5 + x)       *||----------- - -------|  - -------- - ------------------- - ------------|
               ||   ________    5 + x |           2      ________                   3/2 |
               ||  /      2           |    (5 + x)      /      2            /     2\    |
               \\\/  1 - x            /               \/  1 - x  *(5 + x)   \1 - x /    /

$$\left(x + 5\right)^{\operatorname{acos}{\left (x \right )}} \left(- \frac{x \log{\left (x + 5 \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \left(\frac{\log{\left (x + 5 \right )}}{\sqrt{- x^{2} + 1}} - \frac{\operatorname{acos}{\left (x \right )}}{x + 5}\right)^{2} - \frac{2}{\left(x + 5\right) \sqrt{- x^{2} + 1}} - \frac{\operatorname{acos}{\left (x \right )}}{\left(x + 5\right)^{2}}\right)$$

Третья производная

               /                         3                                                                                                                                                         2           \
       acos(x) |  / log(5 + x)   acos(x)\     log(5 + x)   2*acos(x)            3               / log(5 + x)   acos(x)\ /acos(x)             2            x*log(5 + x)\           3*x           3*x *log(5 + x)|
(5 + x)       *|- |----------- - -------|  - ----------- + --------- + -------------------- + 3*|----------- - -------|*|-------- + ------------------- + ------------| - ------------------- - ---------------|
               |  |   ________    5 + x |            3/2           3      ________              |   ________    5 + x | |       2      ________                   3/2 |           3/2                     5/2  |
               |  |  /      2           |    /     2\       (5 + x)      /      2         2     |  /      2           | |(5 + x)      /      2            /     2\    |   /     2\                /     2\     |
               \  \\/  1 - x            /    \1 - x /                  \/  1 - x  *(5 + x)      \\/  1 - x            / \           \/  1 - x  *(5 + x)   \1 - x /    /   \1 - x /   *(5 + x)     \1 - x /     /

$$\left(x + 5\right)^{\operatorname{acos}{\left (x \right )}} \left(- \frac{3 x^{2} \log{\left (x + 5 \right )}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} - \frac{3 x}{\left(x + 5\right) \left(- x^{2} + 1\right)^{\frac{3}{2}}} - \left(\frac{\log{\left (x + 5 \right )}}{\sqrt{- x^{2} + 1}} - \frac{\operatorname{acos}{\left (x \right )}}{x + 5}\right)^{3} + 3 \left(\frac{\log{\left (x + 5 \right )}}{\sqrt{- x^{2} + 1}} - \frac{\operatorname{acos}{\left (x \right )}}{x + 5}\right) \left(\frac{x \log{\left (x + 5 \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{2}{\left(x + 5\right) \sqrt{- x^{2} + 1}} + \frac{\operatorname{acos}{\left (x \right )}}{\left(x + 5\right)^{2}}\right) - \frac{\log{\left (x + 5 \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{3}{\left(x + 5\right)^{2} \sqrt{- x^{2} + 1}} + \frac{2 \operatorname{acos}{\left (x \right )}}{\left(x + 5\right)^{3}}\right)$$