Производная log(acos(2*x))

Вы ввели

log(acos(2*x))

$$\log{\left (\operatorname{acos}{\left (2 x \right )} \right )}$$

Первая производная

          -2           
-----------------------
   __________          
  /        2           
\/  1 - 4*x  *acos(2*x)

$$- \frac{2}{\sqrt{- 4 x^{2} + 1} \operatorname{acos}{\left (2 x \right )}}$$

Вторая производная

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

$$\frac{1}{\operatorname{acos}{\left (2 x \right )}} \left(- \frac{8 x}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{4}{\left(4 x^{2} - 1\right) \operatorname{acos}{\left (2 x \right )}}\right)$$

Третья производная

   /                                                   2                             \
   |      1                    2                   12*x                 6*x          |
-8*|------------- + ------------------------ + ------------- + ----------------------|
   |          3/2             3/2                        5/2              2          |
   |/       2\      /       2\        2        /       2\      /        2\           |
   \\1 - 4*x /      \1 - 4*x /   *acos (2*x)   \1 - 4*x /      \-1 + 4*x / *acos(2*x)/
--------------------------------------------------------------------------------------
                                      acos(2*x)                                       

$$- \frac{1}{\operatorname{acos}{\left (2 x \right )}} \left(\frac{96 x^{2}}{\left(- 4 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{48 x}{\left(4 x^{2} - 1\right)^{2} \operatorname{acos}{\left (2 x \right )}} + \frac{8}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{16}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left (2 x \right )}}\right)$$