chain rule power

Practise chain rule power with an original VectorPaths question, worked explanation and related VCE Methods practice.

2 practice marks

Original practice question

Differentiate $f(x)=(3 x + 2)^{3}$ with respect to $x$.

Worked explanation

• Identify inner and outer functions

  Let $u=3 x + 2$; then $f=u^{3}$.

• Apply the chain rule

  $f\prime(x)=3(3 x + 2)^{2}\times 3=9 \left(3 x + 2\right)^{2}$.

$f\prime(x)=9 \left(3 x + 2\right)^{2}$.

Original VectorPaths practice; not an official VCAA question or marking rubric.