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Question
Find `dy/dx`, if `sqrt(x) + sqrt(y) = sqrt(a)`.
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Solution
`sqrt(x) + sqrt(y) = sqrt(a)`
Differentiating both sides w.r.t. x, we get
`(1)/(2sqrt(x)) + (1)/(2sqrt(y)) * dy/dx = 0`
∴ `(1)/(2sqrt(y)) dy/dx = -(1)/(2sqrt(x))`
∴ `dy/dx = -sqrt(y/x)`.
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