Question

Apply the principle of implicit differentiation to the function x^2y^3+3xy=14 to determine it's derivative

Answer 1

just use the product and chain rules.

x^2y^3+3xy=14
2xy^3 + 3x^2y^2 y' + 3y + 3xy' = 0
(3x^2y^2+3x)y' = -(2xy^3+3y)
y' = -(2xy^3 + 3y) / (3x^2y^2 + 3x)