Learn how to take the derivative of a function with respect to t

The video tutorial explains the process of finding the derivative of a product of two variables using the product rule. It begins with an introduction to derivatives, followed by a detailed explanation of the product rule. The instructor then demonstrates how to apply the rule to solve for the derivative of a product, breaking down the steps for clarity. The tutorial concludes with the final expression for the derivative, emphasizing the change in the function with respect to time.

What is the significance of identifying constants in the expression 2π RH?

• It determines the variable to be differentiated.

• It changes the order of differentiation.

• It helps in simplifying the derivative calculation.

• It eliminates the need for the product rule.

Which rule is applied to differentiate the product of two variables with respect to time?

• Quotient Rule

• Power Rule

• Chain Rule

• Product Rule

In the product rule, what is the derivative of R * H with respect to time?

• dR/dT + dH/dT

• dR/dT * dH/dT

• dR/dT * H + R * dH/dT

• R * H

How is the expression for the change in S with respect to time derived?

• By applying the chain rule to R and H

• By adding the derivatives of R and H

• By multiplying the derivatives of R and H

• By combining the results of the product rule derivatives

What does the final expression 2π HDR/dT + 2π R DH/dT represent?

• The total change in volume

• The change in S with respect to time

• The rate of change of radius

• The rate of change of height