JEE Main 2023MathematicsDifferentiationMediumMCQ

JEE Main 2023 — Differentiation Question with Solution

JEE Main 2023 (06 Apr Shift 1)

Question

If 2xy+3yx=20, then dydx at 2,2 is equal to:

Choose an option

Show full solutionCorrect option: A
Correct answer
A-2+loge83+loge4

Step-by-step explanation

Given,

2xy+3yx=20

Now differentiating both sides w.r.t x, we get

2xyy'lnx+yx+3yxlny+xy·y'=0 here ln=loge

Putting x=2 & y=2, we get

⇒8ln2·y'+1+12lny+y'=0

⇒8ln2·y'+1+12lny+y'=0

⇒y'=-3ln2+22ln2+3

⇒y'=-2+ln83+ln4

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About this question

This is a previous-year question from JEE Main 2023, 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.