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Question
If xy2 = 1, then prove that `2 "dy"/"dx" + y^3`= 0
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Solution
Given xy2 = 1 ....(1)
Differentiating with respect to 'x' we get,
`x*2y "dy"/"dx" + y^2 (1) = 0` ...[using product rule]
Multiplying by y throughout we get,
`2xy^2 "dy"/"dx" + y^3` = 0
`=> 2(1) * "dy"/"dx" + y^3` = 0
`=> 2(1) "dy"/"dx" + y^3 = 0` ...[using (1)]
`=> 2 "dy"/"dx" + y^3` = 0
Hence proved.
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