Производная cot(asin(x))

Вы ввели

cot(asin(x))

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

Первая производная

        2         
-1 - cot (asin(x))
------------------
      ________    
     /      2     
   \/  1 - x      

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

Вторая производная

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

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

Третья производная

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

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