JEE Main 2018MathematicsDifferentiationMediumMCQ

JEE Main 2018 — Differentiation Question with Solution

JEE Main 2018 (16 Apr Online)

Question

If x=2cosec-1t and  y=2sec-1t, t≥1, then dydx is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B-yx

Step-by-step explanation

Given, x=2cosec-1t=2cosec-1t2 and  y=2sec-1t=2sec-1t2, then we have

x·y=2sec−1t+cosec−1t2

And, we know that sec-1x+cosec-1x=π2,

⇒xy=2π4

On differentiating, both sides with respect to x, and applying product rule, we get

xdydx+y=0

⇒dydx=-yx.

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About this question

This is a previous-year question from JEE Main 2018, 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.