2.03 The product rule

Interactive practice questions

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

You may use the substitution $u=3x-2$u=3x−2 and $v=4x-5$v=4x−5 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

select and apply the product rule, quotient rule and chain rule to differentiate functions; express derivatives in simplest and factorised form