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arctan(e^x)
The derivative of the function/ arctan(e^x)

Derivative of arctan(e^x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    / x\
atan\E /
$$\operatorname{atan}{\left(e^{x} \right)}$$
Transform
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    x   
   e    
--------
     2*x
1 + e
$$\frac{e^{x}}{e^{2 x} + 1}$$
Simplify
The second derivative [src] 
/        2*x \   
|     2*e    |  x
|1 - --------|*e 
|         2*x|   
\    1 + e   /   
-----------------
          2*x    
     1 + e
$$\frac{\left(1 - \frac{2 e^{2 x}}{e^{2 x} + 1}\right) e^{x}}{e^{2 x} + 1}$$
Simplify
The third derivative [src] 
/        2*x          4*x  \   
|     8*e          8*e     |  x
|1 - -------- + -----------|*e 
|         2*x             2|   
|    1 + e      /     2*x\ |   
\               \1 + e   / /   
-------------------------------
                 2*x           
            1 + e
$$\frac{\left(1 - \frac{8 e^{2 x}}{e^{2 x} + 1} + \frac{8 e^{4 x}}{\left(e^{2 x} + 1\right)^{2}}\right) e^{x}}{e^{2 x} + 1}$$
Simplify
The graph
Derivative of arctan(e^x)
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