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Question
If x = `y + 1/y`, then `dy/dx` = ____.
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Solution
If x = `y + 1/y`, then `dy/dx = bb(underline(y^2/(y^2 - 1))`.
Explanation:
x = `y + 1/y`
Differentiating both sides w.r.t. x, we get
1 = `dy/dx + ((-1)/y^2). dy/dx`
∴ 1 = `dy/dx (1 - 1/y^2)`
∴ 1 = `dy/dx((y^2 - 1)/y^2)`
∴ `dy/dx = y^2/(y^2 - 1)`
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