New Zealand
Level 8 - NCEA Level 3

# 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
Approx 3 minutes

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.

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

### Outcomes

#### M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

#### 91578

Apply differentiation methods in solving problems