Last updated on Sep 22, 2026

Derivatives of Exponential Functions (AQA A-Level Mathematics): Quizzes

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Derivatives of Exponential Functions

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What is $\frac{d}{dx} e^x$ equal to?

$e^x$

Which base makes an exponential function's derivative equal to itself?

$e \approx 2.718$

What is $\frac{d}{dx} a^x$ for a general base $a > 0$ ?

$a^x \ln(a)$

In $\frac{d}{dx} a^x = a^x \ln(a)$ , what role does $\ln(a)$ play?

Constant multiplier

What is $\frac{d}{dx} e^{u(x)}$ using the chain rule?

$e^{u(x)} \cdot u'(x)$

Find $\frac{dy}{dx}$ for $y = e^{3x}$

$3e^{3x}$

Find $\frac{dy}{dx}$ for $y = 5^x$

$5^x \ln(5)$

Find $\frac{dy}{dx}$ for $y = 2e^{-x^2}$

$-4x e^{-x^2}$

Find $\frac{dy}{dx}$ for $y = 3x \cdot e^{2x}$

$3e^{2x}(1 + 2x)$

Which field uses derivatives of exponentials for modelling growth and decay?

Biology, physics, finance

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Exponential & Logarithms

Laws of Logarithms

Modelling with Exponentials & Logarithms

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Exponential & Logarithms

Laws of Logarithms

Modelling with Exponentials & Logarithms

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Exponential & Logarithms

Laws of Logarithms

Modelling with Exponentials & Logarithms

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Exponential & Logarithms

Laws of Logarithms

Modelling with Exponentials & Logarithms

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