`cot(y) = x - y` Find `dy/dx` by implicit differentiation.

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Chapter 2, 2.5 - Problem 14 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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`coty = x - y`

``Differentiating both sides w.r.t 'x' we get

`-cosec^2(y)*(dy/dx) = 1 - (dy/dx)`

`or, (dy/dx)*[1-cosec^2(y)] = 1`

`or, dy/dx = 1/[1-cosec^2(y)]`

`or, dy/dx = -1/[cosec^2(y) - 1]`

`or, dy/dx = -1/{cot^2(y)}`

`or, dy/dx = -tan^2(y)`

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