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AustraliaVIC
VCE 12 Methods 2023

5.03 The product rule

Interactive practice questions

Differentiate the function $f\left(x\right)=\left(3x-2\right)\left(4x-5\right)$f(x)=(3x2)(4x5).

You may use the substitution $u=3x-2$u=3x2 and $v=4x-5$v=4x5 in your working.

Easy
2min

We want to differentiate $y=x^6\left(x^4+4\right)$y=x6(x4+4) using the product rule.

Let $u=x^6$u=x6 and $v=x^4+4$v=x4+4.

Easy
3min

We want to differentiate $y=x^3\left(x^2+9\right)$y=x3(x2+9).

Easy
5min
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Outcomes

U34.AoS3.3

derivatives of f(x) +/- g(x), f(x) x g(x), f(x)/g(x) and (𝑓 ∘ 𝑔)(𝑥) where f and g are polynomial functions, exponential, circular, logarithmic or power functions and transformations or simple combinations of these functions

U34.AoS3.12

the sum, difference, chain, product and quotient rules for differentiation

U34.AoS3.17

apply the product, chain and quotient rules for differentiation to simple combinations of functions by hand

U34.AoS3.16

find derivatives of polynomial functions and power functions, functions of the form f(ax+b) where f is x^n, sine, cosine; tangent, e^x, or log x base e and simple linear combinations of these, using pattern recognition, or by hand

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