Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 61

Equation of a tangent line to the graph of function f at point (x_0,y_0) is given by y=y_0+f'(x_0)(x-x_0).
The first step to finding equation of tangent line is to calculate the derivative of the given function. To calculate this derivative we will have to use the chain rule (u(v))'=u'(v)cdot v'
y'=1/(1+(x/2)^2)cdot1/2
Now we calculate the value of the derivative at the given point.
y'(2)=1/(2(1+(2/2)^2))=1/2(1+1)=1/4
We now have everything needed to write the equation of the tangent line.
y=pi/4+1/4(x-2)
y=x/4+(pi-2)/4
Graph of the function along with the tangent line can be seen in the image below.