Differentiation and Function Analysis

The video tutorial explains how to differentiate a radical function by first converting it to rational exponents. It introduces the given function and highlights the need to apply the chain rule, identifying the inner function and its derivative. The tutorial then demonstrates using the power rule of differentiation in conjunction with the chain rule, followed by performing substitutions for the inner function and its derivative. Finally, the video simplifies the expression and presents the final solution, including rewriting the denominator as a cube root.

What is the first step in differentiating a radical function?

• Apply the chain rule directly

• Convert to rational exponents

• Use the product rule

• Find the derivative of the inner function

In the given function, what is identified as the inner function U?

• 9 * a 2/3 power

• 2xq + 8

• 6x^2

• f of x

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

• 3x^2

• 6x^2

• 2x^2

• 9x^2

How is the original function expressed in terms of U?

• 9 * U^(1/3)

• 9 * U^2

• 9 * U^3

• 9 * U^(2/3)

What is the simplified form of 9 * 2/3 * 6x^2?

• 36x^2

• 24x^2

• 54x^2

• 18x^2