Understanding Derivatives of Natural Log Functions

The video tutorial explains how to find the derivative of a natural logarithm function using the chain rule. It starts by introducing the derivative formula for natural log functions and identifying the inner function U. The tutorial then calculates the derivative of U, known as U prime, and substitutes these into the derivative formula. Finally, it simplifies the expression to find the derivative of the given function.

What is the derivative formula for the natural log function with respect to x?

• U over U prime

• U prime over U

• U times U prime

• 1 over U times U prime

In the function F(x) = 8 ln(3x^4 + 2), what is the inner function U?

• x^4

• 3x^4 + 2

• 8

• ln(3x^4 + 2)

What is the derivative of the inner function U, where U = 3x^4 + 2?

• 4x^3

• 3x^3

• 12x^3

• 12x^4

After substituting U and U prime, what is the simplified form of the derivative of F(x)?

• 8x^4 / (3x^4 + 2)

• 96x^4 / (3x^4 + 2)

• 8x^3 / (3x^4 + 2)

• 96x^3 / (3x^4 + 2)

What is the role of the constant 8 in the function F(x) = 8 ln(3x^4 + 2) when finding the derivative?

• It is divided by the derivative of ln(U)

• It is subtracted from the derivative of ln(U)

• It is added to the derivative of ln(U)

• It is multiplied by the derivative of ln(U)