Question

If xy² = 1, then prove that `2 "dy"/"dx" + y^3`= 0

Answer 1

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.