Mister Exam

Derivative of atan(sqrt(x))

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

The graph:

from to

Piecewise:

The solution

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