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Derivative Notation and Basic Rules (HSC SSCE Mathematics Advanced): Quizzes

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Derivative Notation and Basic Rules

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What is the derivative of $f(x) = x^5$ using the power rule?

$5x^4$

What is $\frac{dy}{dx}$ if $y = x^{-3}$ ?

$-3x^{-4}$

To differentiate $y = \sqrt{x}$ using the power rule, what should you do first?

Convert to $x^{\frac{1}{2}}$

Which notation emphasizes the derivative as a rate of change?

$\frac{dy}{dx}$

Using the constant multiple rule, what is $\frac{d}{dx}(7x^2)$ ?

$14x$

What is the derivative of $f(x) = x^3 + x^2$ using the sum rule?

$3x^2 + 2x$

What is $f'(x)$ if $f(x) = 3x^4 - 2x^3 + 5x$ ?

$12x^3 - 6x^2 + 5$

What is the derivative of the constant term in $y = 4x^2 - 7$ ?

$0$

Before differentiating $y = \frac{1}{x^4}$ , what form should you use?

$y = x^{-4}$

What should you do first to differentiate $f(x) = \frac{x^3 - x^2}{x}$ ?

Split and simplify the fraction

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Derivative Notation and Basic Rules (HSC SSCE Mathematics Advanced): Quizzes

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What is the derivative of f(x)=x5f(x) = x^5f(x)=x5 using the power rule?

What is dydx\frac{dy}{dx}dxdy​ if y=x−3y = x^{-3}y=x−3?

To differentiate y=xy = \sqrt{x}y=x​ using the power rule, what should you do first?

Which notation emphasizes the derivative as a rate of change?

Using the constant multiple rule, what is ddx(7x2)\frac{d}{dx}(7x^2)dxd​(7x2)?

What is the derivative of f(x)=x3+x2f(x) = x^3 + x^2f(x)=x3+x2 using the sum rule?

What is f′(x)f'(x)f′(x) if f(x)=3x4−2x3+5xf(x) = 3x^4 - 2x^3 + 5xf(x)=3x4−2x3+5x?

What is the derivative of the constant term in y=4x2−7y = 4x^2 - 7y=4x2−7?

Before differentiating y=1x4y = \frac{1}{x^4}y=x41​, what form should you use?

What should you do first to differentiate f(x)=x3−x2xf(x) = \frac{x^3 - x^2}{x}f(x)=xx3−x2​?

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 Flashcards 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

What is the derivative of $f(x) = x^5$ using the power rule?

What is $\frac{dy}{dx}$ if $y = x^{-3}$ ?

To differentiate $y = \sqrt{x}$ using the power rule, what should you do first?

Using the constant multiple rule, what is $\frac{d}{dx}(7x^2)$ ?

What is the derivative of $f(x) = x^3 + x^2$ using the sum rule?

What is $f'(x)$ if $f(x) = 3x^4 - 2x^3 + 5x$ ?

What is the derivative of the constant term in $y = 4x^2 - 7$ ?

Before differentiating $y = \frac{1}{x^4}$ , what form should you use?

What should you do first to differentiate $f(x) = \frac{x^3 - x^2}{x}$ ?