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Question
Find `"dy"/"dx"` for the following function.
x2 – xy + y2 = 1
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Solution
x2 – xy + y2 = 1
Differentiating both side with respect to x,
`"d"/"dx" (x^2) - "d"/"dx" (xy) + "d"/"dx" (y^2) = "d"/"dx"(7)`
`2x - [x "d"/"dx" (y) + y "d"/"dx" (x)] + 2y "dy"/"dx" = 0`
`2x - [x "dy"/"dx" + y * 1] + 2y "dy"/"dx" = 0`
`2x - x"dy"/"dx" - y + 2y "dy"/"dx"` = 0
`"dy"/"dx" [2x - x] = y - 2x`
`"dy"/"dx" = (y - 2x)/(2y - x)`
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