Question

Xy=1, then y2 +dy/dx=

Answer 1

Hello,

If xy = 1 then
y = 1/x

Thus:
dy/dx = -1/x²

And
y² + dy/dx = (1/x)² + (-1/x²) = 1/x² – 1/x² = 0

Answer 2

Answer:

$y^2+\dfrac{dy}{dx}=0$

Step-by-step explanation:

Given: xy = 1

To find: $y^2+\dfrac{dy}{dx}=?$

$xy=1$

$x=\dfrac{1}{y}$

differentiate w.r.t x

$1=-\dfrac{1}{y^2}\cdot \dfrac{dy}{dx}$           (chain rule)

$y^2=-\dfrac{dy}{dx}$

$y^2+\dfrac{dy}{dx}=0$

Hence, the value of given differential equation is 0