Question

Find dy/dx by implicit differentiation for x – y = xy.

Answer 1

Answer:

$\frac{dy}{dx}$ = $\frac{1-y}{1+x}$

Step-by-step explanation:

Differentiate xy using the product rule, then

Given

x - y = xy

1 - $\frac{dy}{dx}$ = x. $\frac{dy}{dx}$ + y. 1 = x$\frac{dy}{dx}$ + y ( subtract 1 from both sides )

- $\frac{dy}{dx}$ = x $\frac{dy}{dx}$ + y - 1 ( subtract x $\frac{dy}{dx}$ from both sides )

- $\frac{dy}{dx}$ - x $\frac{dy}{dx}$ = y - 1 ( multiply through by - 1 )

$\frac{dy}{dx}$ + x$\frac{dy}{dx}$ = 1 - y

$\frac{dy}{dx}$ (1 + x) = 1 - y ← divide both sides by (1 + x)

$\frac{dy}{dx}$ = $\frac{1-y}{1+x}$

Answer 2

Answer:

- \frac{dy}{dx} = x. \frac{dy}{dx}