Производная (acot(x)-1)/(x+1)

Вы ввели

acot(x) - 1
-----------
   x + 1   

$$\frac{\operatorname{acot}{\left (x \right )} - 1}{x + 1}$$

Первая производная

         1           acot(x) - 1
- ---------------- - -----------
  /     2\                    2 
  \1 + x /*(x + 1)     (x + 1)  

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

Вторая производная

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

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

Третья производная

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

$$\frac{1}{x + 1} \left(- \frac{8 x^{2}}{\left(x^{2} + 1\right)^{3}} - \frac{6 x}{\left(x + 1\right) \left(x^{2} + 1\right)^{2}} + \frac{2}{\left(x^{2} + 1\right)^{2}} - \frac{6}{\left(x + 1\right)^{2} \left(x^{2} + 1\right)} - \frac{1}{\left(x + 1\right)^{3}} \left(6 \operatorname{acot}{\left (x \right )} - 6\right)\right)$$