Производная log(acos(x))

Вы ввели

log(acos(x))

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

Первая производная

        -1         
-------------------
   ________        
  /      2         
\/  1 - x  *acos(x)

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

Вторая производная

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

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

Третья производная

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

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