Derivatives and Logarithmic Functions

The video tutorial explains how to find the derivative of the function 3 log base 2 of (2x^2 - 3). It begins by introducing the concept of derivatives and the need to apply the chain rule. The inner function is identified as 2x^2 - 3, and its derivative is calculated. Since the logarithm's base is not e, a specific derivative formula is used. The tutorial walks through the steps of applying this formula, simplifying the expression, and arriving at the final derivative: 12x divided by the product of the natural log of 2 and (2x^2 - 3).

What rule is necessary to apply when finding the derivative of 3 log base 2 of the quantity 2x^2 - 3?

• Product Rule

• Power Rule

• Chain Rule

• Quotient Rule

What is the inner function U in the expression 3 log base 2 of the quantity 2x^2 - 3?

• 2x^2 - 3

• 2x^2 + 3

• x^2 - 3

• 3x^2 - 2

What is the derivative of the inner function U, denoted as U Prime?

• 2x

• 4x

• 6x

• 8x

Which logarithmic base is used in the function 3 log base 2 of U?

• Base 5

• Base e

• Base 10

• Base 2

What is the final expression for the derivative of 3 log base 2 of the quantity 2x^2 - 3?

• 6x / (ln 10 * (2x^2 - 3))

• 12x / (ln 10 * (2x^2 - 3))

• 6x / (ln 2 * (2x^2 - 3))

• 12x / (ln 2 * (2x^2 - 3))