Производная acos(x/(x+5))

Вы ввели

    /  x  \
acos|-----|
    \x + 5/

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

Первая производная

 /  1        x    \ 
-|----- - --------| 
 |x + 5          2| 
 \        (x + 5) / 
--------------------
      ______________
     /         2    
    /         x     
   /   1 - -------- 
  /               2 
\/         (x + 5)  

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

Вторая производная

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

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

Третья производная

             /                     2                                                      \
             |         4*x      3*x                          2                            |
             |    1 - ----- + --------         2 /       x  \              /       x  \   |
             |        5 + x          2      3*x *|-1 + -----|          4*x*|-1 + -----|   |
/       x  \ |                (5 + x)            \     5 + x/              \     5 + x/   |
|-1 + -----|*|6 + -------------------- + ------------------------ + ----------------------|
\     5 + x/ |                2                        2            /        2   \        |
             |               x           /        2   \             |       x    |        |
             |        1 - --------       |       x    |         2   |1 - --------|*(5 + x)|
             |                   2       |1 - --------| *(5 + x)    |           2|        |
             |            (5 + x)        |           2|             \    (5 + x) /        |
             \                           \    (5 + x) /                                   /
-------------------------------------------------------------------------------------------
                                     ______________                                        
                                    /         2                                            
                                   /         x             3                               
                                  /   1 - -------- *(5 + x)                                
                                 /               2                                         
                               \/         (5 + x)                                          

$$\frac{1}{\left(x + 5\right)^{3} \sqrt{- \frac{x^{2}}{\left(x + 5\right)^{2}} + 1}} \left(\frac{x}{x + 5} - 1\right) \left(\frac{3 x^{2} \left(\frac{x}{x + 5} - 1\right)^{2}}{\left(x + 5\right)^{2} \left(- \frac{x^{2}}{\left(x + 5\right)^{2}} + 1\right)^{2}} + \frac{4 x \left(\frac{x}{x + 5} - 1\right)}{\left(x + 5\right) \left(- \frac{x^{2}}{\left(x + 5\right)^{2}} + 1\right)} + 6 + \frac{\frac{3 x^{2}}{\left(x + 5\right)^{2}} - \frac{4 x}{x + 5} + 1}{- \frac{x^{2}}{\left(x + 5\right)^{2}} + 1}\right)$$