Vault Of Euclid

Derivative of a Composite Polynomial Function

The chain rule warmup

If \( y = x^3-2 \) and \( x = 3z^2+5 \), then \( y \) can be considered a function of \( z \). Express \( \frac{dy}{dz} \) in terms of \( z \).
chain-ruledifferentiationcomposite-functionssubstitutioncalculus-iderivativespolynomial-differentiationpower-rule

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What you need first

What this problem tests

Tests the ability to apply the chain rule in Leibniz notation and perform algebraic substitution to reach the required form.

This is a standard introductory problem in Calculus I when learning the chain rule.

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