Understanding the Product Rule in Calculus

Why is the product rule necessary when finding the derivative of the function 2x - 5 and 7x^3 - 3x^2?

• Because the function is a sum of terms.

• Because the function is a difference of terms.

• Because the function is a product of two expressions.

• Because the function is a quotient of two expressions.

What is the derivative of 7x^3?

• 3x^2

• 21x^2

• 7x^2

• 14x^2

What is the derivative of 2x - 5?

• 2

• 0

• 5

• -5

After applying the product rule, what is the next step in simplifying the expression?

• Divide by the highest power of x.

• Distribute and combine like terms.

• Add all terms together.

• Subtract the smaller expression from the larger one.

What common factor can be factored out from the final derivative expression?

• x

• x^4

• x^2

• x^3