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If x^m y^n=(x+y)^(m+n) , prove that (dy)...

If `x^m y^n=(x+y)^(m+n)` , prove that `(dy)/(dx)=y/x` .

Text Solution

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Given `x^{m} y^{n}=(x+y)^{m+n}`

Taking logarithm of both sides we get

`\log (x^{m} \cdot y^{n})=\log (x+y)^{m+n}`

`\Rightarrow \quad \log x^{m}+\log y^{n}=(m+n) \cdot \log (x+y)` ...
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