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1/2arctg((e^x-3)/2)

Derivative of 1/2arctg((e^x-3)/2)

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

The graph:

from to

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The solution

You have entered [src]
    / x    \
    |e  - 3|
atan|------|
    \  2   /
------------
     2      
$$\frac{\operatorname{atan}{\left(\frac{e^{x} - 3}{2} \right)}}{2}$$
  /    / x    \\
  |    |e  - 3||
  |atan|------||
d |    \  2   /|
--|------------|
dx\     2      /
$$\frac{d}{d x} \frac{\operatorname{atan}{\left(\frac{e^{x} - 3}{2} \right)}}{2}$$
The graph
The first derivative [src]
         x       
        e        
-----------------
  /            2\
  |    / x    \ |
  |    \e  - 3/ |
4*|1 + ---------|
  \        4    /
$$\frac{e^{x}}{4 \left(\frac{\left(e^{x} - 3\right)^{2}}{4} + 1\right)}$$
The second derivative [src]
/      /      x\  x\   
|    2*\-3 + e /*e |  x
|1 - --------------|*e 
|                 2|   
|        /      x\ |   
\    4 + \-3 + e / /   
-----------------------
                  2    
         /      x\     
     4 + \-3 + e /     
$$\frac{\left(1 - \frac{2 \left(e^{x} - 3\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4}\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4}$$
The third derivative [src]
/                                                 2     \   
|           2*x         /      x\  x     /      x\   2*x|   
|        2*e          6*\-3 + e /*e    8*\-3 + e / *e   |  x
|1 - -------------- - -------------- + -----------------|*e 
|                 2                2                   2|   
|        /      x\        /      x\    /             2\ |   
|    4 + \-3 + e /    4 + \-3 + e /    |    /      x\ | |   
\                                      \4 + \-3 + e / / /   
------------------------------------------------------------
                                    2                       
                           /      x\                        
                       4 + \-3 + e /                        
$$\frac{\left(1 - \frac{6 \left(e^{x} - 3\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4} - \frac{2 e^{2 x}}{\left(e^{x} - 3\right)^{2} + 4} + \frac{8 \left(e^{x} - 3\right)^{2} e^{2 x}}{\left(\left(e^{x} - 3\right)^{2} + 4\right)^{2}}\right) e^{x}}{\left(e^{x} - 3\right)^{2} + 4}$$
The graph
Derivative of 1/2arctg((e^x-3)/2)