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


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