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  4. If xmyn=(x+y)m+n , then (d y/d x) is

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Q. If $ x^{m}y^{n}=(x+y)^{m+n} $ , then $ \frac{d y}{d x} $ is

UPSEEUPSEE 2008

Solution:

Given, $x^{m} y^{n}=(x+y)^{m+n}$
Taking log on both sides, we get $m \log x+n \log y=(m+n) \log (x+y)$
On differentiating wrt $x$, we get,
$\frac{d y}{d x}=\frac{y}{x}$