JEE Main 2021MathematicsDifferentiationMediumNumerical

JEE Main 2021 — Differentiation Question with Solution

JEE Main 2021 (26 Aug Shift 1)

Question

If y=y(x) is an implicit function of x such that loge(x+y)=4xy, then d2y dx2 at x=0 is equal to

Enter your answer

Show full solutionCorrect answer: 40
Correct answer
40

Step-by-step explanation

Given:

loge(x+y)=4xy

When x=0, then y=1

logex+y=4xy

⇒x+y=e4xy

Now differentiate w.r.t. x

1+y'=e4xy4y+4xy'   …i

At (0,1)⇒y'(0)+1=4⇒y'(0)=3

Now, again differentiate equation (i), we get

y"=e4xy4y+4xy′2+e4xy4y'+4y'+4xy"

At 0,1

y"(0)=1(4×1+0)2+1(4×3+4×3+0)

⇒y"(0)=16+24=40

⇒y"(0)=40

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Differentiation chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2021, 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.