Find the rate of change of demand (\(x\)) of a commodity with respect to its price (\(y\)) if \(y=\frac{5x+7}{2x-13}\)

Q.2 (A) (iii) Find the rate of change of demand (\(x\)) of a commodity with respect to its price (\(y\)) if \(y=\frac{5x+7}{2x-13}\)

Doubtly Asked 28 Oct 2026 Board exam · June 2026 hsc 12th Save WhatsApp Report

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Answer: \(\frac{dx}{dy}=-\frac{(2x-13)^2}{79}\)

By the quotient rule,
\(\frac{dy}{dx}=\frac{(2x-13)(5)-(5x+7)(2)}{(2x-13)^2}=\frac{10x-65-10x-14}{(2x-13)^2}=\frac{-79}{(2x-13)^2}\).

The rate of change of demand with respect to price is \(\frac{dx}{dy}=\frac{1}{dy/dx}=-\frac{(2x-13)^2}{79}\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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