If y = l n x x , then d 2 y d x 2 = 2 x 3 l n x - λ , where λ is

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Question: Answered & Verified by Expert

If

y = \frac{l n x}{x}

, then

\frac{d^{2} y}{d x^{2}} = \frac{2}{x^{3}} (l n x - λ)

, where

λ

is

MathematicsDifferentiationJEE Main

Options:

A $\frac{3}{2}$
B $\frac{2}{3}$
C $\frac{1}{2}$
D $\frac{1}{3}$

Solution:

2055 Upvotes Verified Answer

The correct answer is:

\frac{3}{2}

Using quotient rule, we get,

\frac{d y}{d x} = \frac{1 - l n x}{x^{2}}

∴ \frac{d^{2} y}{d x^{2}} = \frac{(x^{2}) (- \frac{1}{x}) - (1 - l n x) (2 x)}{x^{4}}

= \frac{- 1 - 2 + 2 l n x}{x^{3}}

= \frac{2}{x^{3}} (l n x - (1 + \frac{1}{2}))

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