Dear student,

Our given equation is y = xtan^-1x

So we have to find first derivative or dy/dx.

Now, two functions are multiplied to each other so we will use the product rule of differentiation.

So, dy/ dx = x (1/1+x^2) + tan^-1x (1)

So, our answer is :-

dy/dx = tan^-1x + x/(1+x^2).