Производная acot(cbrt(2*x))

Вы ввели

    /3 _____\
acot\\/ 2*x /

$$\operatorname{acot}{\left (\sqrt[3]{2 x} \right )}$$

Первая производная

        3 ___         
       -\/ 2          
----------------------
   2/3 /     2/3  2/3\
3*x   *\1 + 2   *x   /

$$- \frac{\sqrt[3]{2}}{3 x^{\frac{2}{3}} \left(2^{\frac{2}{3}} x^{\frac{2}{3}} + 1\right)}$$

Вторая производная

  /3 ___                    \
  |\/ 2            2        |
2*|----- + -----------------|
  |  5/3     /     2/3  2/3\|
  \ x      x*\1 + 2   *x   //
-----------------------------
        /     2/3  2/3\      
      9*\1 + 2   *x   /      

$$\frac{\frac{4}{x \left(2^{\frac{2}{3}} x^{\frac{2}{3}} + 1\right)} + \frac{2 \sqrt[3]{2}}{x^{\frac{5}{3}}}}{9 \cdot 2^{\frac{2}{3}} x^{\frac{2}{3}} + 9}$$

Третья производная

   /  3 ___                                   2/3       \
   |5*\/ 2            10                   8*2          |
-2*|------- + ------------------ + ---------------------|
   |   8/3     2 /     2/3  2/3\                       2|
   |  x       x *\1 + 2   *x   /    4/3 /     2/3  2/3\ |
   \                               x   *\1 + 2   *x   / /
---------------------------------------------------------
                       /     2/3  2/3\                   
                    27*\1 + 2   *x   /                   

$$- \frac{1}{27 \cdot 2^{\frac{2}{3}} x^{\frac{2}{3}} + 27} \left(\frac{20}{x^{2} \left(2^{\frac{2}{3}} x^{\frac{2}{3}} + 1\right)} + \frac{16 \cdot 2^{\frac{2}{3}}}{x^{\frac{4}{3}} \left(2^{\frac{2}{3}} x^{\frac{2}{3}} + 1\right)^{2}} + \frac{10 \sqrt[3]{2}}{x^{\frac{8}{3}}}\right)$$