`(x^3)y - x(y^3) = 4` Find `dy/dx` by implicit differentiation.

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hkj1385 eNotes educator| Certified Educator

`(x^3)*y - x*(y^3) = 4`

differentiating

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

`or, (dy/dx)*[(x^3)-3x(y^2)] = (y^3) - 3(x^2)y`

`or, dy/dx = [(y^3) - 3(x^2)y]/[(x^3)-3x(y^2)]`

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