Find the derivative my distributing and getting common denominators AP

The video tutorial guides students through the process of finding the derivative of a function, f(x). It begins with an introduction to the objective, followed by simplifying the function using algebraic techniques. The instructor then applies the power rule to find the derivative and discusses common mistakes. Finally, the video covers rationalizing the expression to achieve the final answer.

What is the first step in finding the derivative of a function according to the teacher?

• Simplify the expression.

• Find the common denominator.

• Apply the power rule directly.

• Rationalize the numerator.

When applying the power rule, what operation is performed on the exponent?

• Add 1 to the exponent.

• Multiply the exponent by 2.

• Divide the exponent by 2.

• Subtract 1 from the exponent.

Why is it important to have common denominators in the expression?

• To simplify the expression further.

• To ensure no radicals are in the numerator.

• To apply the power rule correctly.

• To make the expression more complex.

What is the equivalent of x to the 1/2 in terms of radicals?

• x squared

• Square root of x

• x to the power of 3

• Cube root of x

What is the final form of the expression after rationalizing the numerator?

• 2x to the 1/2

• 6x squared

• x to the 3/2

• 4x to the 1/2