If y = e n x , then d 2 y d x 2 . d 2 x d y 2 is equal to :

If y=enx, then d2ydx2.d2xdy2  is equal to :
  1. ne-nx
  2. -ne-nx
  3. nenx
  4. 1

Solution

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

Asked in: JEE Main 2014 (09 Apr Online)

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