How to determine the derivative of rational expression using power rule

The video tutorial introduces the quotient rule and explains its advantages. It demonstrates how to rewrite polynomials for simplification and then applies derivatives to these simplified expressions. The tutorial concludes with final instructions and remarks, emphasizing the importance of expressing exponents positively.

What is one advantage of using the quotient rule for dividing functions?

• It is only applicable to polynomials.

• It requires more steps.

• It is easier and makes more sense.

• It is more complex.

How can the expression X^3 / X^2 - 3X^2 / X^2 + 4 / X^2 be simplified?

• X - 3 + 4 / X^2

• X^3 - 3 + 4X

• X - 3 + 4X^2

• X^3 - 3X^2 + 4

What is the derivative of a constant?

• Undefined

• 1

• 0

• The constant itself

When applying derivatives, what happens to the exponent of X in the term 4X^-2?

• It decreases by one.

• It remains the same.

• It increases by one.

• It becomes positive.

Why is it important to write exponents as positive?

• It is a mathematical rule.

• It makes calculations easier.

• It is visually appealing.

• It simplifies the expression.