Understanding Derivatives and the Product Rule

Which of the following is NOT a fundamental operation in calculus?

• Subtraction

• Addition

• Composition

• Exponentiation

What is the derivative of a product of two functions according to the product rule?

• The sum of the derivatives

• The product of the derivatives

• The derivative of the first function times the second function plus the first function times the derivative of the second function

• The difference of the derivatives

In the product rule, what does the notation f' represent?

• The integral of f

• The derivative of f

• The function f itself

• The second derivative of f

When multiplying two polynomials before differentiating, what is the first step?

• Divide the terms

• Subtract the exponents

• Multiply each term on the left by each term on the right

• Add the coefficients

What is a common mistake when applying the product rule?

• Applying the sum rule

• Using the chain rule instead

• Forgetting to multiply the derivatives

• Assuming the derivative of a product is the product of the derivatives

How can you test if your product rule formula is correct?

• By using the quotient rule

• By applying it to a simple example and checking the result

• By using the chain rule

• By integrating the functions

When extending the product rule to three functions, what is the first step?

• Apply the chain rule

• Differentiate each function separately

• Use the quotient rule

• Group two functions together and treat them as a single function

What is the derivative of e^x?

• e^x

• 0

• x * e^(x-1)

• 1

In the example of differentiating 17x * cos(x) * e^x, what is the derivative of 17x?

• 0

• 17x

• x

• 17

What pattern is observed when using the product rule for three functions?

• The chain rule is applied

• The product of the derivatives is taken

• The derivative of the sum is the sum of the derivatives

• Each term has all three functions and the derivative of one of them