Q.3 (A) (i) Find dy/dx if y=(x)^x+(a)^x

Answer: dy/dx=x^x(1+log x)+a^xlog a Let u=x^x , v=a^x , so y=u+v and dy/dx=du/dx+dv/dx . log u=xlog x . Differentiating: 1/udu/dx=x·1/x+log x=1+log x⇒du/dx=x^x(1+log x) . dv/dx=a^xlog a . Hence dy/dx=x^x(1+log x)+a^xlog a .

Find \(\frac{dy}{dx}\) if \(y=(x)^x+(a)^x\)

Q.3 (A) (i) Find \(\frac{dy}{dx}\) if \(y=(x)^x+(a)^x\)

Doubtly Asked 28 Oct 2026 Board exam · March 2025 hsc 12th Save WhatsApp Report

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Answer: \(\frac{dy}{dx}=x^x(1+\log x)+a^x\log a\)

Let \(u=x^x\), \(v=a^x\), so \(y=u+v\) and \(\frac{dy}{dx}=\frac{du}{dx}+\frac{dv}{dx}\).

\(\log u=x\log x\). Differentiating: \(\frac{1}{u}\frac{du}{dx}=x\cdot\frac{1}{x}+\log x=1+\log x\Rightarrow\frac{du}{dx}=x^x(1+\log x)\).

\(\frac{dv}{dx}=a^x\log a\).

Hence \(\frac{dy}{dx}=x^x(1+\log x)+a^x\log a\).

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

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Find \(\frac{dy}{dx}\) if \(y=(x)^x+(a)^x\)

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