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Derivative of arcsin((x+1)/2)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
    /x + 1\
asin|-----|
    \  2  /
$$\operatorname{asin}{\left(\frac{x + 1}{2} \right)}$$
asin((x + 1)/2)
The graph
The first derivative [src]
          1          
---------------------
       ______________
      /            2 
     /      (x + 1)  
2*  /   1 - -------- 
  \/           4     
$$\frac{1}{2 \sqrt{1 - \frac{\left(x + 1\right)^{2}}{4}}}$$
The second derivative [src]
       1 + x       
-------------------
                3/2
  /           2\   
  |    (1 + x) |   
8*|1 - --------|   
  \       4    /   
$$\frac{x + 1}{8 \left(1 - \frac{\left(x + 1\right)^{2}}{4}\right)^{\frac{3}{2}}}$$
The third derivative [src]
                2   
       3*(1 + x)    
  4 + ------------  
                 2  
          (1 + x)   
      1 - --------  
             4      
--------------------
                 3/2
   /           2\   
   |    (1 + x) |   
32*|1 - --------|   
   \       4    /   
$$\frac{4 + \frac{3 \left(x + 1\right)^{2}}{1 - \frac{\left(x + 1\right)^{2}}{4}}}{32 \left(1 - \frac{\left(x + 1\right)^{2}}{4}\right)^{\frac{3}{2}}}$$