16:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 17:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 15:T482,{"@context":"https://schema.org","@type":"Quiz","name":"Kcet 2026 Differentiation PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/kcet/questions/2026/mathematics/differentiation/jt-mr7eh8z2","educationalLevel":"Entrance exam preparation","about":"Kcet / Mathematics / Differentiation","hasPart":{"@type":"Question","name":"Kcet 2026 Differentiation PYQ with Solution","text":"If \\sqrt{x} \\sqrt[3]{y} = (x + y)^n and x\\dfrac{dy}{dx} - y = 0, then n =","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"C"},"comment":{"@type":"Comment","text":"Given, \\sqrt{x}\\sqrt[3]{y}=(x+y)^n and x\\dfrac{dy}{dx}-y=0 From the second equation, x\\dfrac{dy}{dx}=y So, \\dfrac{dy}{dx}=\\dfrac{y}{x} Now take logarithm on both sides of \\sqrt{x}\\sqrt[3]{y}=(x+y)^n We get \\log\\left(x^{1/2}y^{1/3}\\right)=\\log\\left((x+y)^n\\right) Using laws of logarithms, \\dfrac{1}{2}\\log x+\\dfrac{1}{3}\\log y=n\\log(x+y) Differentiate both sides with respect to x: \\dfrac{1}{2x}+\\dfrac{1}{3}\\cdot \\dfrac{1}{y}\\dfrac{dy}{dx} = n\\cdot \\dfrac{1+\\dfrac{dy}{dx}}{x+y} Now substitute \\dfr..."}}}18:T48c,

Given,

$$ \sqrt{x}\sqrt[3]{y}=(x+y)^n $$

and

$$ x\dfrac{dy}{dx}-y=0 $$

From the second equation,

$$ x\dfrac{dy}{dx}=y $$

So,

$$ \dfrac{dy}{dx}=\dfrac{y}{x} $$

Now take logarithm on both sides of

$$ \sqrt{x}\sqrt[3]{y}=(x+y)^n $$

We get

$$ \log\left(x^{1/2}y^{1/3}\right)=\log\left((x+y)^n\right) $$

Differentiation

Continue this paper

Similar Differentiation PYQs

More practice from this question