If `x y=4`,prove that `x((dy)/(dx)+y^2)=3y`

Explanation

We have, `x y=4`

``
Rightarrow y=frac{4}{x}

``
Differentiate it with respect to `x`,

`frac{d y}{d x}=frac{d}{d x}(frac{4}{x})`

`Rightarrow frac{d y}{d x}=4 frac{d}{d x}(x^{-1})`

`Rightarrow frac{d y}{d x}=4(-1 times x^{-1-1})`

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