Производная (x-cos(x))/acos(x)

Вы ввели

x - cos(x)
----------
 acos(x)  

$$\frac{x - \cos{\left (x \right )}}{\operatorname{acos}{\left (x \right )}}$$

Первая производная

1 + sin(x)        x - cos(x)     
---------- + --------------------
 acos(x)        ________         
               /      2      2   
             \/  1 - x  *acos (x)

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

Вторая производная

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

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

Третья производная

                                                                                                                            2                                    
               x - cos(x)         6*(1 + sin(x))           3*cos(x)           6*(x - cos(x))        3*x*(1 + sin(x))     3*x *(x - cos(x))      6*x*(x - cos(x)) 
-sin(x) + ------------------- - ------------------ + ------------------- + -------------------- + ------------------- + ------------------- + -------------------
                  3/2           /      2\     2         ________                   3/2                    3/2                   5/2                    2         
          /     2\              \-1 + x /*acos (x)     /      2            /     2\        3      /     2\              /     2\              /      2\      2   
          \1 - x /   *acos(x)                        \/  1 - x  *acos(x)   \1 - x /   *acos (x)   \1 - x /   *acos(x)   \1 - x /   *acos(x)   \-1 + x / *acos (x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                             acos(x)                                                                             

$$\frac{1}{\operatorname{acos}{\left (x \right )}} \left(\frac{3 x^{2} \left(x - \cos{\left (x \right )}\right)}{\left(- x^{2} + 1\right)^{\frac{5}{2}} \operatorname{acos}{\left (x \right )}} + \frac{6 x \left(x - \cos{\left (x \right )}\right)}{\left(x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left (x \right )}} + \frac{3 x \left(\sin{\left (x \right )} + 1\right)}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}{\left (x \right )}} + \frac{x - \cos{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}{\left (x \right )}} + \frac{6 x - 6 \cos{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left (x \right )}} - \sin{\left (x \right )} - \frac{6 \sin{\left (x \right )} + 6}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left (x \right )}} + \frac{3 \cos{\left (x \right )}}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left (x \right )}}\right)$$