JEE Main 2014MathematicsDifferentiationMediumMCQ

JEE Main 2014 — Differentiation Question with Solution

JEE Main 2014 (09 Apr Online)

Question

If y=enx, then d2ydx2.d2xdy2  is equal to :

Choose an option

Show full solutionCorrect option: B
Correct answer
B-ne-nx

Step-by-step explanation

y=enx ⇒ dydx=nenx ∵ddxeax=aeax

    ⇒ d2ydx2=n2enx

dydx=nenx⇒dxdy=1nenx=1ne-nx

           d2xdy2=ddydxdy

             =ddxdxdy·dxdy

               =ddx1ne-nx·e-nxn

               =1n-ne-nx·e-nxn

               =-1ne-2nx

⇒   d2ydx2.d2xdy2=n2enx×-e-2nxn

                       =-ne-nx

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About this question

This is a previous-year question from JEE Main 2014, 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.