Understanding the Chain Rule in Calculus

The video tutorial explains how to find H Prime of 3 using the chain rule. It starts by introducing the problem and the concept of composite functions. The chain rule is then explained, highlighting the differentiation of the outer function evaluated at the inner function, followed by multiplying by the derivative of the inner function. The tutorial proceeds with calculating H Prime of 3 by substituting values from a table, determining G of 3 and G Prime of 3, and finally finding F Prime of 1 to conclude that H Prime of 3 equals 8.

What is the main objective of the problem discussed in the video?

• To find the value of H' of 3 for a composite function.

• To determine the value of G' of 3.

• To solve for x in the equation H(x) = 0.

• To calculate the integral of H(x).

What is the chain rule used for in calculus?

• To integrate composite functions.

• To find the limit of a function.

• To differentiate composite functions.

• To solve linear equations.

In the chain rule, what do you do after differentiating the outer function?

• Multiply by the derivative of the inner function.

• Add the derivative of the inner function.

• Divide by the derivative of the inner function.

• Subtract the derivative of the inner function.

What is the value of G(3) as per the table?

• 2

• 3

• 1

• 0

What is the value of G'(3) according to the table?

• 1

• 4

• 2

• 3

After finding G(3) and G'(3), what is the next step in applying the chain rule?

• Solve for x in the equation F(x) = 0.

• Calculate the integral of F(x).

• Find F'(G(3)) using the table.

• Determine the limit of F(x) as x approaches 3.

What is the value of F'(1) as per the table?

• 3

• 4

• 5

• 6

What is the final value of H' of 3?

• 6

• 8

• 7

• 9