Implicit differentiation using the product rule

The video tutorial explains the application of the product rule in calculus. It begins with an introduction to the product rule, followed by a detailed step-by-step application of the rule to differentiate expressions involving x and y squared. The tutorial also covers how to take derivatives of y squared with respect to x, including the use of dy/dx. Finally, it demonstrates how to rearrange terms to finalize the derivative expression.

What is the initial expression set up for differentiation using the product rule?

• D over DX of y^2 minus X

• D over DX of X plus y^2

• D over DX of y^2 times X

• D over DX of X times y^2

What is the result of differentiating D over DX of X?

• 1

• X

• y^2

• 0

How is the derivative of y^2 rewritten with respect to X?

• 2y

• y^2 times X

• X times DY over DX

• 2y times DY over DX

What is the final expression after applying the product rule completely?

• X plus y^2

• y^2 plus 2XY DY over DX

• y^2 plus 2XY

• 2XY plus y^2

Why is it important to include DY over DX when differentiating y^2 with respect to X?

• To eliminate X from the equation

• To simplify the expression

• To account for the change in y with respect to X

• Because y^2 is a constant