Year 12 Maths Advanced MAV-12-04 Checkpoint 1

Checkpoint Quiz 1

This checkpoint covers Differentiating $e^x$, Differentiating $a^x$, and Differentiating $\ln x$ (Lessons 1–3).

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Quick Review

Differentiating $e^x$: $\dfrac{d}{dx}(e^x) = e^x$, the only function equal to its own derivative. For composite exponentials, the chain rule gives $\dfrac{d}{dx}(e^{kx}) = ke^{kx}$, bring down the derivative of the exponent.
Differentiating $a^x$: $\dfrac{d}{dx}(a^x) = a^x \ln a$. Since $a^x = e^{x\ln a}$, the chain rule introduces a $\ln a$ correction factor out front. When $a = e$, $\ln e = 1$ and the correction disappears, giving back $e^x$.
Differentiating $\ln x$: $\dfrac{d}{dx}(\ln x) = \dfrac{1}{x}$, the simplest reciprocal function. Its rate of change decreases as $x$ grows.
Chain rule for logarithms: $\dfrac{d}{dx}(\ln g(x)) = \dfrac{g'(x)}{g(x)}$. The numerator is always the derivative of what is inside the logarithm.

5 random questions from the Checkpoint 1 bank, feedback shown immediately

Great work finishing Checkpoint 1.

If you struggled with any questions, go back to Lessons 1–3 to review the concepts before moving on.

Tick when you're ready to continue to Lesson 4.