If xy = 1, prove that

We are given with an equation xy = 1, we have to prove that + y² = 0 by using the given equation we will first find the value of and we will put this in the equation we have to prove, so by differentiating the equation on both sides with respect to x, we get,

By using product rule, we get,

y(1) + x = 0

Or we can further solve it by using the given equation,

By putting this value in the L.H.S. of the equation, we get,

–y² + y² = 0 = R.H.S.