`sqrt(xy) = x - 4y` Find `dy/dx` by implicit differentiation.

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Chapter 2, Review - Problem 80 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`sqrt(xy)=x-4y`

Differentiating both sides with respect to x,

`(1/2)(xy)^(-1/2)d/dx(xy)=1-4y'`

`1/(2sqrt(xy))(xy'+y)=1-4y'`

`xy'+y=2sqrt(xy)(1-4y')`

`xy'+y=2sqrt(xy)-8sqrt(xy)*y'`

`xy'+8sqrt(xy)*y'=2sqrt(xy)-y`

`(x+8sqrt(xy))y'=2sqrt(xy)-y`

`y'=(2sqrt(xy)-y)/(x+8sqrt(xy))`

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