Chain rule and gradient at a point

Practise chain rule and gradient at a point with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $g(x)=(3x-2)^4$. (a) Find $g\prime(x)$. [2 marks] (b) Find the point and gradient when $x=1$. [2 marks]

Worked explanation

• Part (a)

  Differentiate the outer fourth power and multiply by the inner derivative 3: $4(3x-2)^3\times3$.

• Part (b)

  $g(1)=1^4=1$ and $g\prime(1)=12(1)^3=12$.

(a) $12(3x-2)^3$.; (b) Point $(1,1)$; gradient $12$.

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