Quick questions on Further differentiation and applications: WACE Year 12 Mathematics Methods Unit 3

Q: What is product rule?

If y = u v then dydx = u'v + uv'.

Q: What is quotient rule?

If y = uv then dydx = u'v - uv'v^2.

Q: What is quotient rule numerator order?

It is u'v - uv', not uv' - u'v. The wrong order flips the sign of the whole derivative.

Q: What is not classifying the stationary point?

Solving f'(x) = 0 only locates candidates. You must confirm whether each is a maximum, minimum or inflection before answering an optimisation question.

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is product rule?

Show answer

y = u v

then

\dfrac{dy}{dx} = u'v + uv'

What is quotient rule?

Show answer

y = \dfrac{u}{v}

then

\dfrac{dy}{dx} = \dfrac{u'v - uv'}{v^2}

What is quotient rule numerator order?

Show answer

It is

u'v - uv'

, not

uv' - u'v

. The wrong order flips the sign of the whole derivative.

What is not classifying the stationary point?

Show answer

Solving

f'(x) = 0

only locates candidates. You must confirm whether each is a maximum, minimum or inflection before answering an optimisation question.

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