1.

If y = tan–1 (2x/ 1 - x2), find (dy/dx).

Answer»

Given y = tan–1 (2x/ 1 - x2)

Put x = tan θ 

⇒ θ = tan–1x

y = tan–1 (2 tan θ/ 1 - tan2 θ)

= tan–1 (tan 2θ) 

= 2θ 

= 2tan–1

differentiating w.r.to 'x' on both sides, we have 

(dy/dx) = 2(d/dx) = tan−1 x

= 2(1/1 + x2)

∴ (dy/dx) = (2/ 1 + x2)



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