Производная log(acos(5*x))

Вы ввели

log(acos(5*x))

$$\log{\left (\operatorname{acos}{\left (5 x \right )} \right )}$$

Первая производная

          -5            
------------------------
   ___________          
  /         2           
\/  1 - 25*x  *acos(5*x)

$$- \frac{5}{\sqrt{- 25 x^{2} + 1} \operatorname{acos}{\left (5 x \right )}}$$

Вторая производная

   /          1                   5*x      \
25*|---------------------- - --------------|
   |/         2\                        3/2|
   |\-1 + 25*x /*acos(5*x)   /        2\   |
   \                         \1 - 25*x /   /
--------------------------------------------
                 acos(5*x)                  

$$\frac{1}{\operatorname{acos}{\left (5 x \right )}} \left(- \frac{125 x}{\left(- 25 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{25}{\left(25 x^{2} - 1\right) \operatorname{acos}{\left (5 x \right )}}\right)$$

Третья производная

     /                                                     2                               \
     |      1                      2                   75*x                   15*x         |
-125*|-------------- + ------------------------- + -------------- + -----------------------|
     |           3/2              3/2                         5/2               2          |
     |/        2\      /        2\        2        /        2\      /         2\           |
     \\1 - 25*x /      \1 - 25*x /   *acos (5*x)   \1 - 25*x /      \-1 + 25*x / *acos(5*x)/
--------------------------------------------------------------------------------------------
                                         acos(5*x)                                          

$$- \frac{1}{\operatorname{acos}{\left (5 x \right )}} \left(\frac{9375 x^{2}}{\left(- 25 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{1875 x}{\left(25 x^{2} - 1\right)^{2} \operatorname{acos}{\left (5 x \right )}} + \frac{125}{\left(- 25 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{250}{\left(- 25 x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left (5 x \right )}}\right)$$