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Question
Find `"dy"/"dx"` for the following function
xy – tan(xy)
Solution
Given xy – tan(xy)
Differentiating both sides with respect to x, we get
`"d"/"dx" = (xy) = "d"/"dx" tan (xy)`
`x "d"/"dx" (y) + y "d"/"dx" (x) = sec^2 (xy) "d"/"dx" (xy)`
`"x" "dy"/"dx" + y(1) = sec^2 (xy) [x "dy"/"dx" + y "d"/"dx" (x)]`
`"x" "dy"/"dx" + y = sec^2(xy) [x "dy"/"dx" + y]`
`"x" "dy"/"dx" + y = x sec^2 (xy) "dy"/"dx" + y sec^2 (xy)`
`"x" "dy"/"dx" - x sec^2 (xy) "dy"/"dx" = y sec^2 (xy) - y`
`"dy"/"dx" [x - x sec^2 (xy)] = y[sec^2 (xy) - 1]`
`"dy"/"dx" = (y[sec^2 (xy) - 1])/(x[1 - sec^2 (xy)])`
`= y/x (-1) = (-y)/x`
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