Last updated on Sep 20, 2026

The Chain Rule (VCE SSCE Mathematical Methods): Quizzes

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The Chain Rule

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What is $q(x) = (x^3 + 1)^2$ an example of?

A composite function

In $q(x) = (x^3 + 1)^2$ , what is the inside function?

$g(x) = x^3 + 1$

What is the chain rule formula in Leibniz notation?

$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$

The chain rule is: derivative of outside times derivative of what?

Derivative of inside

When does the chain rule work?

When both functions are differentiable

For $u = 4x^3 - 5x$ , what is $\frac{du}{dx}$ ?

$12x^2 - 5$

For $y = \frac{16}{3x^2 + 1}$ at $(1, 4)$ , what is the gradient?

$-6$

Why use chain rule instead of expanding $(x^3 + 1)^{30}$ ?

Chain rule is much more efficient

How should $y = \frac{16}{3x^2 + 1}$ be rewritten for chain rule?

$y = 16(3x^2 + 1)^{-1}$

What should you identify first before applying chain rule?

Inside and outside functions

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