Производная acos(x)/asin(x)

Вы ввели

acos(x)
-------
asin(x)

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

                                              2                                                                               2                                 
       1                 6                 3*x             acos(x)              6*acos(x)                6*x               3*x *acos(x)          6*x*acos(x)    
- ----------- - -------------------- - ----------- - ------------------- - -------------------- + ------------------ - ------------------- + -------------------
          3/2           3/2                    5/2           3/2                   3/2                     2                   5/2                    2         
  /     2\      /     2\        2      /     2\      /     2\              /     2\        3      /      2\            /     2\              /      2\      2   
  \1 - x /      \1 - x /   *asin (x)   \1 - x /      \1 - x /   *asin(x)   \1 - x /   *asin (x)   \-1 + x / *asin(x)   \1 - x /   *asin(x)   \-1 + x / *asin (x)
----------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                            asin(x)                                                                             

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