`x^3 - xy + y^2 = 7` Find `dy/dx` by implicit differentiation.

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Chapter 2, 2.5 - Problem 5 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: `x^3-xy+y^2=7`

`3x^2-[xdy/dx+y(1)]+2ydy/dx=0`

`3x^2-xdy/dx-y+2ydy/dx=0`

`-xdy/dx+2ydy/dx=-3x^2+y`

`xdy/dx-2ydy/dx=3x^2-y`

`dy/dx(x+2y)=3x^2-y`

`dy/dx=(3x^2-y)/(x+2y)`

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