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AQA A Level - Exponential & Log Basics

Exponential Functions, Logs & Log Laws

AS Revision AS Revision

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Exponential Functions (AS) Exponential Functions (AS)
Logarithms (AS) Logarithms (AS)

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Using exponential functions

Using logarithms to any base

Exponential Derivatives (AS) Exponential Derivatives (AS)

Explore relationship between exponential functions and their derivatives

Exponential Graphs (AS) Exponential Graphs (AS)
Gradient of $e^{x}$ (AS) Gradient of $e^{x}$ (AS)

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Exponential Graphs: $a^{x}$

The graph of

f (x) = a^{x}

is shown in blue, together with its tangent and gradient at a sample point in red.

By considering the gradient at x = 0, 1, 2, 3, can you predict what the gradient function of

f (x) = a^{x}

is?

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Gradients of $a^{x}$ and $e^{x}$

Compare the graph of

f (x) = a^{x}

with the graph of its gradient function,

f^{'} (x)

.
Adjust the value of a till the the two curves coincide.

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AQA A Level - Exponential & Log Basics

Exponential Functions, Logs & Log Laws

Using exponential functions

Using logarithms to any base

Explore relationship between exponential functions and their derivatives

Exponential Graphs: $a^{x}$

Gradients of $a^{x}$ and $e^{x}$

A Level Maths Settings

Current A Level Syllabus

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AQA A Level - Exponential & Log Basics

Exponential Functions, Logs & Log Laws

AQA AS Syllabus Content - F1-5

Using exponential functions

Video Context

Using logarithms to any base

Video Context

Explore relationship between exponential functions and their derivatives

Exponential Graphs: ax

Notes

Gradients of ax and ex

Notes

A Level Maths Settings

Current A Level Syllabus

Current Stage

Current Question Difficulty

Current Calculator

Exponential Graphs: $a^{x}$

Gradients of $a^{x}$ and $e^{x}$