JEE Main2014MathematicsDifferentiationActual

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

Options

An e - n x
B- n e - n x
Cn e n x
D1

Correct answer

B. - n e - n x

Step-by-step solution

y = e n x  ⇒  d y d x = n e n x ∵ d d x e a x = a e a x ⇒  d 2 y d x 2 = n 2 e n x d y d x = n e n x ⇒ d x d y = 1 n e n x = 1 n e - n x d 2 x d y 2 = d d y d x d y = d d x d x d y · d x d y = d d x 1 n e - n x · e - n x n = 1 n - n e - n x · e - n x n = - 1 n e - 2 n x ⇒    d 2 y d x 2 . d 2 x d y 2 = n 2 e n x × - e - 2 n x n = - n e - n x

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