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Leni [432]
3 years ago
5

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

Mathematics
2 answers:
frez [133]3 years ago
8 0

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}

Crazy boy [7]3 years ago
4 0

Answer:

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

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