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WAMath MethodsSyllabus dot point

How do we differentiate a function that is a product or a quotient of two simpler functions?

Establish and apply the product rule and the quotient rule to differentiate products and quotients of functions

WACE Year 12 Mathematics Methods Unit 3 the product and quotient rules: their statements, when to use each, applying them to polynomial, exponential and trigonometric factors, with worked SCSA-style examples and the numerator order trap.

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  1. What this dot point is asking
  2. The product rule
  3. The quotient rule
  4. Choosing between rewriting and the quotient rule

What this dot point is asking

SCSA Unit 3 establishes two of the three combining rules for differentiation. This dot point asks you to recognise product and quotient structures and apply the correct rule, which is examined heavily in the calculator-free section where by-hand fluency is tested.

The product rule

When a function is a product of two factors that each depend on xx, you cannot simply multiply the derivatives. The product rule accounts for both factors changing.

The quotient rule

When a function is one expression divided by another, the quotient rule applies. The numerator order matters: the derivative of the top times the bottom comes first.

Choosing between rewriting and the quotient rule

A quotient can sometimes be rewritten as a product with a negative power, then differentiated with the product or chain rule. For instance xcos⁡x=xsec⁡x\dfrac{x}{\cos x}=x\sec x or 1x2=x−2\dfrac{1}{x^{2}}=x^{-2}. Choose whichever path is cleaner; for a simple power in the denominator, rewriting is usually faster than the quotient rule.