JEE Main 2020MathematicsDifferentiationHardMCQ

JEE Main 2020 — Differentiation Question with Solution

JEE Main 2020 (05 Sep Shift 2)

Question

The derivative of tan-11+x2-1x with respect to tan-12x1-x21-2x2 at x=12 is :

Choose an option

Show full solutionCorrect option: D
Correct answer
D310

Step-by-step explanation

Let x=tanθ
y1=tan-1secθ-1tanθ=tan-1tanθ2=θ2=12tan-1x
x=sinϕ,  y2=tan-12sinϕcosϕcos2ϕ=tan-1(tan2ϕ)=2ϕ=2sin-1x

dy1dy2=dy1/dxdy2/dx=11+x2·122·11-x2
=1-x241+x2=1-1441+14=310

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About this question

This is a previous-year question from JEE Main 2020, covering the Differentiation chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.