`x^3 - 3(x^2)y + 2x(y^2) = 12` Find `dy/dx` by implicit differentiation.

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Chapter 2, 2.5 - Problem 9 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`x^3-3x^2y+2xy^2=12`

Differentiating both sides with respect to x,

`3x^2-3(x^2dy/dx+yd/dx(x^2))+2(x(2y)dy/dx+y^2)=0`

`3x^2-3(x^2dy/dx+y(2x))+4xydy/dx+2y^2=0`

`3x^2-3x^2dy/dx-6xy+4xydy/dx+2y^2=0`

`(4xy-3x^2)dy/dx+3x^2-6xy+2y^2=0`

`(4xy-3x^2)dy/dx=6xy-3x^2-2y^2`

`dy/dx=(6xy-3x^2-2y^2)/(4xy-3x^2)`

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