Understanding Derivatives of Square Root Functions

The video tutorial explains how to find the derivative of a square root function using the chain rule. It begins by rewriting the square root as a rational exponent and identifying the inner function. The tutorial then applies the power rule, including the chain rule, to differentiate the function. After substituting the inner function and its derivative, the expression is simplified. The final derivative is presented in both fractional and radical forms.

What is the first step in finding the derivative of a square root function using the chain rule?

• Rewrite the square root using a rational exponent

• Simplify the expression

• Directly apply the power rule

• Find the derivative of the outer function

In the context of the chain rule, what is the inner function U for the expression 3x^2 + 1?

• x^2 + 1

• 6x

• 3x^2 + 1

• 3x^2

How do you find the derivative of the inner function U = 3x^2 + 1?

• Differentiate to get 2x

• Differentiate to get 3x

• Differentiate to get 1

• Differentiate to get 6x

What is the result of simplifying 6 * 12 * 6x in the derivative expression?

• 72x

• 54x

• 18x

• 36x

How can the expression be rewritten in radical form?

• By writing the denominator as the square root of 3x^2 + 1

• By writing the numerator as the square root of 3x^2 + 1

• By writing the expression as a cube root

• By writing the entire expression as a square root