JEE Main 2024 · Mathematics · Differentiation and Application of Derivatives · medium

Let y=x^x with x>0. The value of dy/dx at x=1 is

Single correct option

Let

y=x^x

with

x>0

. The value of

\dfrac{dy}{dx}

x=1

Show answer and solution

Answer: (D) $1$

Take logs:

\ln y=x\ln x

, so

\dfrac{y'}{y}=\ln x+1

and

y'=x^x(1+\ln x)

. At

x=1

1\cdot(1+0)=1

. Treating it as a power rule gives

x\cdot x^{x-1}=1

only by accident; the correct method is logarithmic differentiation.

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