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The derivative of the function/ arcsin(sqrt(x)+1)

Derivative of arcsin(sqrt(x)+1)

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

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The solution

You have entered [src] 
    /  ___    \
asin\\/ x  + 1/
asin⁡(x+1)\operatorname{asin}{\left(\sqrt{x} + 1 \right)} 
asin(sqrt(x) + 1)
The graph
02468-8-6-4-2-10100.02-0.02
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
              1               
------------------------------
            __________________
           /                2 
    ___   /      /  ___    \  
2*\/ x *\/   1 - \\/ x  + 1/
12x1−(x+1)2\frac{1}{2 \sqrt{x} \sqrt{1 - \left(\sqrt{x} + 1\right)^{2}}}
Simplify
The second derivative [src] 
                    ___      
   1          1 + \/ x       
- ---- + --------------------
   3/2     /               2\
  x        |    /      ___\ |
         x*\1 - \1 + \/ x / /
-----------------------------
         __________________  
        /                2   
       /      /      ___\    
   4*\/   1 - \1 + \/ x /
x+1x(1−(x+1)2)−1x3241−(x+1)2\frac{\frac{\sqrt{x} + 1}{x \left(1 - \left(\sqrt{x} + 1\right)^{2}\right)} - \frac{1}{x^{\frac{3}{2}}}}{4 \sqrt{1 - \left(\sqrt{x} + 1\right)^{2}}}
Simplify
The third derivative [src] 
                                                                           2     
                                       /      ___\              /      ___\      
 3                1                  3*\1 + \/ x /            3*\1 + \/ x /      
---- + ----------------------- - --------------------- + ------------------------
 5/2        /               2\      /               2\                          2
x       3/2 |    /      ___\ |    2 |    /      ___\ |        /               2\ 
       x   *\1 - \1 + \/ x / /   x *\1 - \1 + \/ x / /    3/2 |    /      ___\ | 
                                                         x   *\1 - \1 + \/ x / / 
---------------------------------------------------------------------------------
                                   __________________                            
                                  /                2                             
                                 /      /      ___\                              
                             8*\/   1 - \1 + \/ x /
−3(x+1)x2(1−(x+1)2)+1x32(1−(x+1)2)+3(x+1)2x32(1−(x+1)2)2+3x5281−(x+1)2\frac{- \frac{3 \left(\sqrt{x} + 1\right)}{x^{2} \left(1 - \left(\sqrt{x} + 1\right)^{2}\right)} + \frac{1}{x^{\frac{3}{2}} \left(1 - \left(\sqrt{x} + 1\right)^{2}\right)} + \frac{3 \left(\sqrt{x} + 1\right)^{2}}{x^{\frac{3}{2}} \left(1 - \left(\sqrt{x} + 1\right)^{2}\right)^{2}} + \frac{3}{x^{\frac{5}{2}}}}{8 \sqrt{1 - \left(\sqrt{x} + 1\right)^{2}}}
Simplify
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