How to write the equation of the tangent line with implicit differentiation

The video tutorial covers implicit differentiation, focusing on finding derivatives using the chain and product rules. The instructor demonstrates solving for dy/dx by applying these rules and simplifying expressions. The tutorial concludes with calculating the slope at a specific point and writing the equation of the line.

What is the primary goal when dealing with implicit differentiation in this context?

• To find the value of x

• To determine the slope of the tangent line

• To eliminate the variable y

• To solve for y

Which mathematical rule is primarily used in the initial steps of finding the derivative?

• Sum Rule

• Power Rule

• Product Rule

• Quotient Rule

What is the significance of substituting known values of x and y in the equation?

• It helps in finding the value of y

• It simplifies the equation and makes solving for dy/dx easier

• It is used to check the accuracy of the equation

• It eliminates the need for differentiation

What is the result of simplifying the equation to find dy/dx?

• dy/dx equals 13/9

• dy/dx equals 9/13

• dy/dx equals 1

• dy/dx equals 0

What is the final form of the equation of the slope at the point (3,1)?

• y - 3 = 9/13(x - 1)

• y - 3 = 13/9(x - 1)

• y - 1 = 9/13(x - 3)

• y - 1 = 13/9(x - 3)