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

Derivative of atan(sqrt(1+sqrt(x)))

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

The graph:

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The solution

You have entered [src] 
    /   ___________\
    |  /       ___ |
atan\\/  1 + \/ x  /
atan⁡(x+1)\operatorname{atan}{\left(\sqrt{\sqrt{x} + 1} \right)} 
atan(sqrt(1 + sqrt(x)))
The graph
02468-8-6-4-2-101002
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                1                 
----------------------------------
           ___________            
    ___   /       ___  /      ___\
4*\/ x *\/  1 + \/ x  *\2 + \/ x /
14xx+1(x+2)\frac{1}{4 \sqrt{x} \sqrt{\sqrt{x} + 1} \left(\sqrt{x} + 2\right)}
Simplify
The second derivative [src] 
 / 2           1               2      \ 
-|---- + ------------- + -------------| 
 | 3/2     /      ___\     /      ___\| 
 \x      x*\1 + \/ x /   x*\2 + \/ x // 
----------------------------------------
           ___________                  
          /       ___  /      ___\      
     16*\/  1 + \/ x  *\2 + \/ x /
−2x(x+2)+1x(x+1)+2x3216x+1(x+2)- \frac{\frac{2}{x \left(\sqrt{x} + 2\right)} + \frac{1}{x \left(\sqrt{x} + 1\right)} + \frac{2}{x^{\frac{3}{2}}}}{16 \sqrt{\sqrt{x} + 1} \left(\sqrt{x} + 2\right)}
Simplify
The third derivative [src] 
 12            3                 6                  8                 12                      4              
---- + ----------------- + -------------- + ----------------- + -------------- + ----------------------------
 5/2                   2    2 /      ___\                   2    2 /      ___\    3/2 /      ___\ /      ___\
x       3/2 /      ___\    x *\1 + \/ x /    3/2 /      ___\    x *\2 + \/ x /   x   *\1 + \/ x /*\2 + \/ x /
       x   *\1 + \/ x /                     x   *\2 + \/ x /                                                 
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                                              ___________                                                    
                                             /       ___  /      ___\                                        
                                        64*\/  1 + \/ x  *\2 + \/ x /
12x2(x+2)+6x2(x+1)+8x32(x+2)2+4x32(x+1)(x+2)+3x32(x+1)2+12x5264x+1(x+2)\frac{\frac{12}{x^{2} \left(\sqrt{x} + 2\right)} + \frac{6}{x^{2} \left(\sqrt{x} + 1\right)} + \frac{8}{x^{\frac{3}{2}} \left(\sqrt{x} + 2\right)^{2}} + \frac{4}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right) \left(\sqrt{x} + 2\right)} + \frac{3}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{12}{x^{\frac{5}{2}}}}{64 \sqrt{\sqrt{x} + 1} \left(\sqrt{x} + 2\right)}
Simplify
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