GATE 2025 MN – Question 13

Engineering Mathematics · Calculus · 1 mark · Multiple choice

For $y=x^x$ with x>0, find dy/dx.

$x^x(\ln x+1)$
$x\,x^{x-1}$
$x(x-1)$
$x\ln x$

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Correct answer: (A) $x^x(\ln x+1)$

Explanation

Take logarithms: ln y=x ln x. Differentiate to get y′/y=ln x+1. Multiplying by y=xˣ yields xˣ(ln x+1), A. The usual constant-power rule alone does not apply because both the base and exponent vary.

GATE 2025 MN – Question 13

Explanation

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