Understanding the Product Rule and Derivatives

Why is the product rule necessary for differentiating the function e^(3x) * ln(x^2 - 5)?

• Because it involves a sum of functions

• Because it involves a product of two functions

• Because it involves a quotient of functions

• Because it involves a constant function

What is the derivative of ln(x^2 - 5) with respect to x?

• x/(x^2 - 5)

• 2x/(x^2 - 5)

• 2/(x^2 - 5)

• 1/(x^2 - 5)

How do you find the derivative of e^(3x)?

• Multiply e^(3x) by 1

• Multiply e^(3x) by x

• Multiply e^(3x) by 3

• Multiply e^(3x) by ln(3x)

What common factor can be factored out from the derivative expression of the function e^(3x) * ln(x^2 - 5)?

• e^(3x)

• 3x

• ln(x^2 - 5)

• x^2 - 5

What is the final simplified form of the derivative of the function e^(3x) * ln(x^2 - 5)?

• e^(3x) * (2/(x^2 - 5) + 3 * ln(x^2 - 5))

• e^(3x) * (x/(x^2 - 5) + 3 * ln(x^2 - 5))

• e^(3x) * (2x/(x^2 - 5) + ln(x^2 - 5))

• e^(3x) * (2x/(x^2 - 5) + 3 * ln(x^2 - 5))