Q.1 (A) (i) If y=sqrt[3]a²+x² then dy/dx = _____. A. 2/3x(a²+x²)^(-2/3) B. 2/3x(a²+x²)^(2/3) C. 2/3(a²+x²)^(-2/3) D. 2/3(a²+x²)^(2/3)

Answer: A. 2/3x(a²+x²)^(-2/3) Answer: (a) 2/3x(a²+x²)^(-2/3) y=(a²+x²)^(1/3) . By the chain rule, dy/dx=1/3(a²+x²)^(-2/3)·d/dx(a²+x²)=1/3(a²+x²)^(-2/3)· 2x=2/3x(a²+x²)^(-2/3) .

If \(y=\sqrt[3]{a^2+x^2}\) then \(\frac{dy}{dx}\) = _____.

Q.1 (A) (i) If \(y=\sqrt[3]{a^2+x^2}\) then \(\frac{dy}{dx}\) = _____.

A. \(\frac{2}{3}x(a^2+x^2)^{-\frac{2}{3}}\)

B. \(\frac{2}{3}x(a^2+x^2)^{\frac{2}{3}}\)

C. \(\frac{2}{3}(a^2+x^2)^{-\frac{2}{3}}\)

D. \(\frac{2}{3}(a^2+x^2)^{\frac{2}{3}}\)

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

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Answer: A. \(\frac{2}{3}x(a^2+x^2)^{-\frac{2}{3}}\)

Answer: (a) \(\frac{2}{3}x(a^2+x^2)^{-\frac{2}{3}}\)

\(y=(a^2+x^2)^{1/3}\). By the chain rule, \(\frac{dy}{dx}=\frac{1}{3}(a^2+x^2)^{-2/3}\cdot\frac{d}{dx}(a^2+x^2)=\frac{1}{3}(a^2+x^2)^{-2/3}\cdot 2x=\frac{2}{3}x(a^2+x^2)^{-2/3}\).

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

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If \(y=\sqrt[3]{a^2+x^2}\) then \(\frac{dy}{dx}\) = _____.

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