Learn how to take the derivative by using the product rule

The video tutorial explains the application of the product rule in calculus, focusing on differentiating functions. It demonstrates how to simplify expressions and highlights the importance of understanding different forms of answers, especially in multiple-choice scenarios. The tutorial emphasizes combining like terms and achieving a common denominator for simplification.

What is the derivative of F(x) = X^(1/2)?

• 1/2 X^(1/2)

• X^(-1/2)

• X^(1/2)

• 1/2 X^(-1/2)

Which of the following is the correct expression for G(x)?

• X^2 + 1

• 1 + X

• X - 1

• X^2 - 1

When applying the product rule, what is the initial expression for H'(x)?

• F(x) * G(x)

• 2X * F'(x) * G(x) + G'(x) * F(x)

• F'(x) + G'(x)

• 2X * G'(x) * F(x)

Why is it important to simplify expressions in multiple-choice questions?

• To avoid using fractions

• To confuse the test-taker

• To match the expected answer format

• To make the expression longer

What is the simplified form of the expression after combining like terms?

• X^(1/2) + 2X

• X + 3X

• X + 3X / 2X^(1/2)

• 1 + X / 2X^(1/2)