`y = arctan(x/2) , (2, pi/4)` Find an equation of the tangent line to the graph of the function at the given point

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`

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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.