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### Differentiation Rules

#### Quotient Rule

###### Where is it used?

The product rule is used where an equation that requires differentiation consists of two separate equations divided from each other.

###### What is the Formula?

Where g(x) is equation on the numerator and f(x) is the equation on the denominator and g'(x) is the differentiation of g(x) and f'(x) is the differentiation of f(x). You do not need to remember this formula as it is not included in your formula sheet, but it is highly recommended that you do so.

###### Worked Example

In this example, we will differentiate y=(2x^3+5)/(4x+2x^2)

Step 1: Determine the equations g(x), g'(x), f(x) and f'(x).

Step 2: Substitute g(x), g'(x), f(x) and f'(x) into the quotient rule formula.

Step 3: Expand the numerator and denominator.

Step 4: Simplify the equation.

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