Differentiation Rules and Mnemonics

This video tutorial covers four essential differentiation rules: the power rule, product rule, quotient rule, and chain rule. Each rule is explained with its general form and illustrated with examples. The tutorial emphasizes the importance of understanding these rules for differentiating functions and provides mnemonic aids to help remember them. The video concludes with a brief overview of all the rules discussed.

Which of the following is NOT one of the four main differentiation rules discussed?

• Chain Rule

• Power Rule

• Sum Rule

• Product Rule

What is the result of differentiating x^3 using the power rule?

• 3x

• x^3

• x^2

• 3x^2

When differentiating a polynomial like 2x^2 + 3x + 4, what happens to the constant term?

• It becomes 1

• It remains unchanged

• It becomes 0

• It doubles

How can the square root of x be rewritten for differentiation using the power rule?

• x^(3/2)

• x^(-1/2)

• x^(1/2)

• x^2

What is the general form of the product rule?

• f(x) * g(x)

• f'(x) / g'(x)

• f'(x) * g(x) + f(x) * g'(x)

• f(x) / g(x)

In the product rule, what is the derivative of the product of x^2 and 3x?

• 6x^2

• 9x^2

• 3x^2

• x^3

What is the mnemonic to remember the quotient rule?

• Low D High minus High D Low, square the bottom and away we go

• Multiply the outside by the derivative of the inside

• First times derivative of the second plus second times derivative of the first

• Drop the exponent and subtract one

What is the derivative of (x^2 + 2) / (3x + 1) using the quotient rule?

• x^2 - 2x + 3

• 3x^2 + 2x - 6

• 2x + 3

• 6x^2 - 3x

What is the general form of the chain rule?

• Derivative of the sum of functions

• Low D High minus High D Low

• Derivative of the outside times the derivative of the inside

• Derivative of the first plus derivative of the second

How do you apply the chain rule to (x^2 + 3)^5?

• 2x(x^2 + 3)^5

• 5(x^2 + 3)^4

• 5(x^2 + 3)^5 * 2x

• 5(x^2 + 3)^4 * 2x