Take the derivative of area with respect to t

The video tutorial explains the concept of derivatives with respect to time, using the area of a rectangle as an example. It introduces the product rule in calculus and demonstrates its application in deriving the rate of change of area. The tutorial concludes by deriving the final equation and highlighting the pattern in the process.

What is the initial concept introduced when differentiating with respect to time?

• The perimeter of a triangle

• The area of a rectangle

• The area of a circle

• The volume of a cube

Why is the product rule necessary in this context?

• Because the area is a sum of two functions

• Because the area is a quotient of two functions

• Because the area is a product of two functions

• Because the area is a difference of two functions

What does the product rule help us find in this scenario?

• The quotient of the derivatives

• The sum of the derivatives

• The product of the derivatives

• The derivative of the product

What is the final expression for the derivative of the area with respect to time?

• LDW over DT plus WDL over DT

• LDW over DT minus WDL over DT

• WDL over DT plus LDW over DT

• WDL over DT minus LDW over DT

What pattern should be noticed in the differentiation process?

• The pattern of addition

• The pattern of multiplication

• The pattern of division

• The pattern of subtraction