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Derivative of atan(e^x-3)/2

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

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The solution

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