If $ y=\left(1+\frac{1}{x}\right)^{x} $, then $ \frac{d y}{d x} $ is equal to

$ \left(1+\frac{1}{x}\right)^{x}\left[\log \left(1+\frac{1}{x}\right)\right] $

$ \left(x+\frac{1}{x}\right)^{x}\left[\log (x-1)-\frac{x}{x+1}\right] $

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

y=\left(1+\frac{1}{x}\right)^{x}

, then

\frac{d y}{d x}

is equal to

View answer and explanation

Correct option: A

\left(1+\frac{1}{x}\right)^{x}\left[\log \left(1+\frac{1}{x}\right)-\frac{1}{1+x}\right]

Option A (

\left(1+\frac{1}{x}\right)^{x}\left[\log \left(1+\frac{1}{x}\right)-\frac{1}{1+x}\right]

) is correct because it is the result of logarithmic differentiation.

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