Производная cot(x)^(asin(x))

Решение

Вы ввели [src]

   asin(x)   
cot       (x)

$$\cot^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}$$

d /   asin(x)   \
--\cot       (x)/
dx

$$\frac{d}{d x} \cot^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}$$

Преобразовать

Подробное решение

Не могу найти шаги в поиске этой производной.

Но производная

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

Ответ:

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

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Первая производная [src]

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

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

Упростить

Вторая производная [src]

              /                                       2                                                          2                             \
              |/                /       2   \        \                                              /       2   \               /       2   \  |
   asin(x)    ||  log(cot(x))   \1 + cot (x)/*asin(x)|      /       2   \           x*log(cot(x))   \1 + cot (x)/ *asin(x)    2*\1 + cot (x)/  |
cot       (x)*||- ----------- + ---------------------|  + 2*\1 + cot (x)/*asin(x) + ------------- - ---------------------- - ------------------|
              ||     ________           cot(x)       |                                       3/2              2                 ________       |
              ||    /      2                         |                               /     2\              cot (x)             /      2        |
              \\  \/  1 - x                          /                               \1 - x /                                \/  1 - x  *cot(x)/

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

Упростить

Третья производная [src]

              /                                         3                                                           /                                                       2                             \                                                                       2                   3                                             2                             \
              |  /                /       2   \        \                    /                /       2   \        \ |                                          /       2   \               /       2   \  |     /       2   \                                        /       2   \       /       2   \               2                 /       2   \                /       2   \ |
   asin(x)    |  |  log(cot(x))   \1 + cot (x)/*asin(x)|    log(cot(x))     |  log(cot(x))   \1 + cot (x)/*asin(x)| |  /       2   \           x*log(cot(x))   \1 + cot (x)/ *asin(x)    2*\1 + cot (x)/  |   6*\1 + cot (x)/     /       2   \                    3*\1 + cot (x)/     2*\1 + cot (x)/ *asin(x)   3*x *log(cot(x))   4*\1 + cot (x)/ *asin(x)   3*x*\1 + cot (x)/ |
cot       (x)*|- |- ----------- + ---------------------|  + ----------- - 3*|- ----------- + ---------------------|*|2*\1 + cot (x)/*asin(x) + ------------- - ---------------------- - ------------------| + --------------- - 4*\1 + cot (x)/*asin(x)*cot(x) - ------------------- - ------------------------ + ---------------- + ------------------------ - ------------------|
              |  |     ________           cot(x)       |            3/2     |     ________           cot(x)       | |                                   3/2              2                 ________       |        ________                                         ________                      3                         5/2               cot(x)                    3/2       |
              |  |    /      2                         |    /     2\        |    /      2                         | |                           /     2\              cot (x)             /      2        |       /      2                                         /      2     2              cot (x)              /     2\                                    /     2\          |
              \  \  \/  1 - x                          /    \1 - x /        \  \/  1 - x                          / \                           \1 - x /                                \/  1 - x  *cot(x)/     \/  1 - x                                        \/  1 - x  *cot (x)                                \1 - x /                                    \1 - x /   *cot(x)/

$$\left(- \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{\cot{\left(x \right)}} - \frac{\log{\left(\cot{\left(x \right)} \right)}}{\sqrt{- x^{2} + 1}}\right)^{3} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{asin}{\left(x \right)} - 3 \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{\cot{\left(x \right)}} - \frac{\log{\left(\cot{\left(x \right)} \right)}}{\sqrt{- x^{2} + 1}}\right) \left(2 \left(\cot^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \operatorname{asin}{\left(x \right)}}{\cot^{2}{\left(x \right)}} + \frac{x \log{\left(\cot{\left(x \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{\sqrt{- x^{2} + 1} \cot{\left(x \right)}}\right) + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \operatorname{asin}{\left(x \right)}}{\cot{\left(x \right)}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \operatorname{asin}{\left(x \right)}}{\cot^{3}{\left(x \right)}} + \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right)}{\sqrt{- x^{2} + 1}} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\sqrt{- x^{2} + 1} \cot^{2}{\left(x \right)}} + \frac{3 x^{2} \log{\left(\cot{\left(x \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} - \frac{3 x \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \cot{\left(x \right)}} + \frac{\log{\left(\cot{\left(x \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}\right) \cot^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}$$

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Производная cot(x)^(asin(x))

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