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Implicit differentiation of 3xy^2

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You need the product rule, and also the Chain Rule.
Derivative of 3x is just 3
Derivative of y^2 is 2y*y' (2 times y times 'y prime')
Derivative of 3x is just 3
Derivative of y^2 is 2y*y' (2 times y times 'y prime')