JEE Main 2019MathematicsDifferentiationMediumMCQ

JEE Main 2019 — Differentiation Question with Solution

JEE Main 2019 (12 Jan Shift 2)

Question

Let f be a differentiable function such that f1=2 and f'x=fx for all x∈R. If hx=ffx, then h'1 is equal to :

Choose an option

Show full solutionCorrect option: C
Correct answer
C 4e

Step-by-step explanation

Given hx=ffx

⇒h'x=f'fx.f'x

⇒h'x=ffx.fx  ...1 (as f'x=fx) 

Now f'x=fx

⇒f'xfx=1

Integrating both sides with respect to x, we get

lnfx=x+c

⇒fx=k.ex

⇒fx=2e. ex     ...2  ∵ f1=2

Putting x=1 in equation 1, we get

h'1=ff1.f1=f2.2=2.2ee2=4e (using equation 2)

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About this question

This is a previous-year question from JEE Main 2019, 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.