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 $f(x)=(2 x - 1)^{4}$ with respect to $x$.

Worked explanation

• Identify inner and outer functions

  Let $u=2 x - 1$; then $f=u^{4}$.

• Apply the chain rule

  $f\prime(x)=4(2 x - 1)^{3}\times 2=8 \left(2 x - 1\right)^{3}$.

$f\prime(x)=8 \left(2 x - 1\right)^{3}$.

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