How to find the derivative of an expression then simplifying

The video tutorial explains the function G of X, simplifies it, and finds its derivative. The instructor discusses how to rewrite the derivative for multiple choice tests, emphasizing the importance of algebraic manipulation to achieve the correct form. The final answer is presented with a detailed explanation.

What is the simplified form of the expression G(x) = x^(1/2) * x - 1?

• x^(3/2) + x^(1/2)

• x^(2) - x^(1/2)

• x^(1/2) - x

• x^(3/2) - x^(1/2)

When finding the derivative of G(x), what is the coefficient of the x term in the derivative?

• 1/2

• 3/2

• 2

• 1

Which of the following is a common mistake when simplifying the derivative of G(x)?

• Ignoring the constant term

• Using incorrect exponents

• Not combining like terms

• Forgetting to multiply by the square root of x

What is the final simplified form of the derivative for a multiple-choice test?

• 3sqrt(x) - 1 over 2x

• 3sqrt(x) - 1 over 2sqrt(x)

• 3x - 1 over 2sqrt(x)

• 3x - 1 over 2x

Why is it important to rewrite the derivative using common denominators?

• To eliminate square roots

• To simplify the calculation

• To match typical multiple-choice answers

• To make it easier to integrate