Mister Exam

Derivative of atan(5*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
atan(5*x)
$$\operatorname{atan}{\left(5 x \right)}$$
atan(5*x)
The graph
The first derivative [src]
    5    
---------
        2
1 + 25*x 
$$\frac{5}{25 x^{2} + 1}$$
The second derivative [src]
   -250*x   
------------
           2
/        2\ 
\1 + 25*x / 
$$- \frac{250 x}{\left(25 x^{2} + 1\right)^{2}}$$
The third derivative [src]
    /            2 \
    |       100*x  |
250*|-1 + ---------|
    |             2|
    \     1 + 25*x /
--------------------
               2    
    /        2\     
    \1 + 25*x /     
$$\frac{250 \left(\frac{100 x^{2}}{25 x^{2} + 1} - 1\right)}{\left(25 x^{2} + 1\right)^{2}}$$
The graph
Derivative of atan(5*x)