Question

A curve is defined by the equation x^2y^3+4x+2y=12. Find dy/dx in terms of x and y.

Answer 1

x^2y^3+4x+2y=12

use the product rule as needed:

2x y^3 + 3x^2y^2 y' + 4 + 2y' = 0
y'(3x^2 y^2 + 2) = -2xy^3 - 4

y' is thus

-2(xy^3 + 2)
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3x^2 y^2 + 2