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8.08 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

Differentiate the function $g\left(t\right)=\left(2t^3-3\right)\left(3-t\right)$g(t)=(2t33)(3t). You may use the substitutions $u=2t^3-3$u=2t33 and $v=3-t$v=3t.

Easy
2min

Differentiate the function $g\left(y\right)=\left(7y^4-y^2\right)\left(y^2-5\right)$g(y)=(7y4y2)(y25). You may use the substitutions $u=7y^4-y^2$u=7y4y2 and $v=y^2-5$v=y25.

Easy
5min

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
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Outcomes

MA11-1

uses algebraic and graphical techniques to solve, and where appropriate, compare alternative solutions to problems

MA11-5

interprets the meaning of the derivative, determines the derivative of functions and applies these to solve simple practical problems

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