Implicit Differentiation Techniques

The video tutorial explains how to use implicit differentiation to find the derivative dydx for a given equation. It begins by setting up the problem and differentiating both sides of the equation with respect to x, applying the chain rule where necessary. The tutorial then demonstrates how to solve for dydx by isolating it on one side of the equation and factoring out common terms. Finally, the solution is simplified to express dydx in terms of x and y.

What is the initial equation given for implicit differentiation?

• y^2 + 4x^3 = 9x - 3y^2

• y^2 + 4x^3 = 9y - 3x^2

• y^2 + 4x^2 = 9y - 3x^3

• y^3 + 4x^2 = 9y - 3x^2

When differentiating a term that only contains x, how do we proceed?

• Multiply by dy/dx

• Differentiate normally

• Use the chain rule

• Use integration

What rule is applied when differentiating terms involving y?

• Power rule

• Chain rule

• Quotient rule

• Product rule

What is the derivative of y^2 with respect to x?

• 2y

• y * dy/dx

• 2y * dy/dx

• 2x * dy/dx

What is the derivative of 4x^3 with respect to x?

• 4x^2

• 12x

• 12x^2

• 3x^2

How do we handle dy/dx terms on both sides of the equation?

• Divide them

• Add them together

• Subtract them from both sides

• Multiply them

What is the common factor that is factored out when solving for dy/dx?

• 9

• x

• 2y

• dy/dx

What is the final expression for dy/dx?

• (-12x^2 - 6x) / (2y - 9)

• (12x^2 - 6x) / (2y - 9)

• (12x^2 + 6x) / (2y + 9)

• (-12x^2 + 6x) / (2y + 9)

What operation is performed to isolate dy/dx in the final step?

• Multiplication

• Subtraction

• Addition

• Division

What is the purpose of using implicit differentiation in this context?

• To integrate the equation

• To simplify the equation

• To solve for dy/dx

• To find the value of x