Last updated on Oct 23, 2026

Euler’s Number and Derivatives (HSC SSCE Mathematics Advanced): Flashcards

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Euler's Number and Derivatives

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Type of number that Euler's number $e$ is

Irrational number

Approximate value of $e$

$2.71828$

Formula for derivative of $e^x$

$\frac{d}{dx}(e^x) = e^x$

$\frac{d}{dx}(e^x)$

$e^x$

Value of $e^0$

$1$

Derivative of $e^x$ at $x = 0$

$1$

Gradient of $y = e^x$ at $x = 1$

$e$

What equals function value on $y = e^x$ at any point

Rate of change (derivative)

Gradient at any point on $y = e^x$

$e^x$ (the y-coordinate)

Definition of derivative

Gradient function of $f(x)$ , denoted $f'(x)$

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Euler’s Number and Derivatives (HSC SSCE Mathematics Advanced): Flashcards

Practise the cards

Type of number that Euler's number eee is

Approximate value of eee

Formula for derivative of exe^xex

ddx(ex)\frac{d}{dx}(e^x)dxd​(ex)

Value of e0e^0e0

Derivative of exe^xex at x=0x = 0x=0

Gradient of y=exy = e^xy=ex at x=1x = 1x=1

What equals function value on y=exy = e^xy=ex at any point

Gradient at any point on y=exy = e^xy=ex

Definition of derivative

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Quizzes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Type of number that Euler's number $e$ is

Approximate value of $e$

Formula for derivative of $e^x$

$\frac{d}{dx}(e^x)$

Value of $e^0$

Derivative of $e^x$ at $x = 0$

Gradient of $y = e^x$ at $x = 1$

What equals function value on $y = e^x$ at any point

Gradient at any point on $y = e^x$