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The derivative of the function/ e^arctg(sqrt(4x-1))

Derivative of e^arctg(sqrt(4x-1))

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
     /  _________\
 atan\\/ 4*x - 1 /
E
eatan⁡(4x−1)e^{\operatorname{atan}{\left(\sqrt{4 x - 1} \right)}} 
E^atan(sqrt(4*x - 1))
The graph
02468-8-6-4-2-1010010
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The first derivative [src] 
     /  _________\
 atan\\/ 4*x - 1 /
e                 
------------------
       _________  
 2*x*\/ 4*x - 1
eatan⁡(4x−1)2x4x−1\frac{e^{\operatorname{atan}{\left(\sqrt{4 x - 1} \right)}}}{2 x \sqrt{4 x - 1}}
Simplify
The second derivative [src] 
                                                           /  __________\
/        1                1                 1       \  atan\\/ -1 + 4*x /
|- ------------- - ---------------- + --------------|*e                  
|            3/2         __________   4*x*(-1 + 4*x)|                    
\  (-1 + 4*x)      2*x*\/ -1 + 4*x                  /                    
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                                    x
(−1(4x−1)32+14x(4x−1)−12x4x−1)eatan⁡(4x−1)x\frac{\left(- \frac{1}{\left(4 x - 1\right)^{\frac{3}{2}}} + \frac{1}{4 x \left(4 x - 1\right)} - \frac{1}{2 x \sqrt{4 x - 1}}\right) e^{\operatorname{atan}{\left(\sqrt{4 x - 1} \right)}}}{x}
Simplify
The third derivative [src] 
                                                                                                                  /  __________\
/      6                1                 2                 3                 3                  1         \  atan\\/ -1 + 4*x /
|------------- + --------------- + --------------- - --------------- - --------------- + ------------------|*e                  
|          5/2    2   __________               3/2                 2      2                 2           3/2|                    
\(-1 + 4*x)      x *\/ -1 + 4*x    x*(-1 + 4*x)      2*x*(-1 + 4*x)    4*x *(-1 + 4*x)   8*x *(-1 + 4*x)   /                    
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                                                               x
(6(4x−1)52−32x(4x−1)2+2x(4x−1)32−34x2(4x−1)+1x24x−1+18x2(4x−1)32)eatan⁡(4x−1)x\frac{\left(\frac{6}{\left(4 x - 1\right)^{\frac{5}{2}}} - \frac{3}{2 x \left(4 x - 1\right)^{2}} + \frac{2}{x \left(4 x - 1\right)^{\frac{3}{2}}} - \frac{3}{4 x^{2} \left(4 x - 1\right)} + \frac{1}{x^{2} \sqrt{4 x - 1}} + \frac{1}{8 x^{2} \left(4 x - 1\right)^{\frac{3}{2}}}\right) e^{\operatorname{atan}{\left(\sqrt{4 x - 1} \right)}}}{x}
Simplify
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