Differentiate w.r.t. tan^-1x when

we have

Let us Assume, p= and q = tan^-1x

And, put x= tan θ

So,

,

Substitute the vaue of θ , we get

Now, differentiate p w.r.t x

-----(i)

Now, for q= tan^-1 x

Differentiate q w.r.t. x

----(ii)

Now, for dp/dq, from equation (i) and (ii)

Hence, dp/dq=1/2