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atan(e^(3*x))

Derivative of atan(e^(3*x))

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

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Piecewise:

The solution

You have entered [src]
    / 3*x\
atan\E   /
$$\operatorname{atan}{\left(e^{3 x} \right)}$$
atan(E^(3*x))
The graph
The first derivative [src]
    3*x 
 3*e    
--------
     6*x
1 + e   
$$\frac{3 e^{3 x}}{e^{6 x} + 1}$$
The second derivative [src]
  /        6*x \     
  |     2*e    |  3*x
9*|1 - --------|*e   
  |         6*x|     
  \    1 + e   /     
---------------------
            6*x      
       1 + e         
$$\frac{9 \left(1 - \frac{2 e^{6 x}}{e^{6 x} + 1}\right) e^{3 x}}{e^{6 x} + 1}$$
The third derivative [src]
   /        6*x         12*x  \     
   |     8*e         8*e      |  3*x
27*|1 - -------- + -----------|*e   
   |         6*x             2|     
   |    1 + e      /     6*x\ |     
   \               \1 + e   / /     
------------------------------------
                   6*x              
              1 + e                 
$$\frac{27 \left(1 - \frac{8 e^{6 x}}{e^{6 x} + 1} + \frac{8 e^{12 x}}{\left(e^{6 x} + 1\right)^{2}}\right) e^{3 x}}{e^{6 x} + 1}$$
The graph
Derivative of atan(e^(3*x))