chain rule

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

1 practice marks

Original practice question

Let $y = (x^2 + 2x)^{3}$. Find $\dfrac{dy}{dx}$.

Worked explanation

• Identify chain rule: y = f(u) where u = g(x)

  \[y = (x^2 + 2x)^{3}, \quad u = x^2 + 2x\]

• dy/dx = dy/du × du/dx

  \[\dfrac{dy}{dx} = 6 x^{2} \left(x + 1\right) \left(x + 2\right)^{2}\]

6*x**2*(x + 1)*(x + 2)**2

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