Q.1 (C)(i) If y = x · log x then d²y/dx² = ____.

Answer: 1/x dy/dx = x · 1/x + log x · 1 = 1 + log x. Differentiating again, d²y/dx² = 0 + 1/x = 1/x.

Chapter: Differentiation· Mathematics & Statistics (Commerce) Part 1

If \(y = x \cdot \log x\) then \(\dfrac{d^2y}{dx^2} =\) ____.

Q.1 (C)(i) If \(y = x \cdot \log x\) then \(\dfrac{d^2y}{dx^2} =\) ____.

Doubtly Asked 29 Oct 2026 Board exam · July 2024 hsc 12th Save WhatsApp Report

1 answer

Best answer

Answer: \(\dfrac{1}{x}\)

\(\dfrac{dy}{dx} = x \cdot \dfrac{1}{x} + \log x \cdot 1 = 1 + \log x\). Differentiating again, \(\dfrac{d^2y}{dx^2} = 0 + \dfrac{1}{x} = \dfrac{1}{x}\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

Was this answer helpful?

If \(y = x \cdot \log x\) then \(\dfrac{d^2y}{dx^2} =\) ____.

1 answer

Your answer