NDA 2025 Maths · Mathematics · Derivatives · medium

The derivative of ln x with respect to e^x at x=1 is

Single correct option

The derivative of

\ln x

with respect to

e^x

x=1

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Answer: (C) $\dfrac1e$

\frac{d(\ln x)}{d(e^x)}=\frac{d(\ln x)/dx}{d(e^x)/dx}=\frac{1/x}{e^x}

. At

x=1

this is

\frac1e

. The value

e

inverts the ratio,

1

\frac{d\ln x}{dx}

1

alone, and

\frac1{e^2}

squares the denominator. Always divide the derivatives, numerator first.

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