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Question
Fill in the Blank
If 0 = log(xy) + a, then `"dy"/"dx" = (-"y")/square`
Solution
If 0 = log(xy) + a, then `"dy"/"dx" = (-"y")/"x"`
Explanation:
0 = log(xy) + a
∴ log(xy) = - a
∴ log x + log y = - a
Differentiating both sides w.r.t.x, we get
`1/"x" + 1/"y" "dy"/"dx" = 0`
∴ `1/"y" * "dy"/"dx" = - 1/"x"`
∴ `"dy"/"dx" = (-"y")/"x"`
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