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All 9 Flashcards — Product rule
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Question
State the product rule.
Answer
(uv)' = u'v + uv'.
Question
What is the first step in using the product rule?
Answer
Label u and v, then find u' and v'.
Question
In words, what is the product rule?
Answer
Differentiate the first times the second, plus the first times the derivative of the second.
Question
Is (uv)' equal to u'v'?
Answer
No — that's a common error; it's u'v + uv'.
Question
When does a product also need the chain rule?
Answer
When one factor is a composite, like e^(2x) or sin(3x).
Question
Differentiate x·eˣ.
Answer
1·eˣ + x·eˣ = eˣ(1 + x).
Question
Differentiate x²·sin x.
Answer
2x·sin x + x²·cos x.
Question
Why factorise a product-rule answer?
Answer
It is usually neater and reveals common factors (e.g. eˣ or a bracket).
Question
Differentiate x·(x + 4) with the product rule.
Answer
1·(x+4) + x·1 = 2x + 4.
Read the notes
Full study notes for Product rule
Topic 5.6 hub
Chain, product & quotient
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Math AA SL exam skills
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