Last updated on Oct 24, 2026

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Differentiating Expressions

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What does the derivative of a function represent?

The slope of the function's graph

In the general rule $f(x)=ax^n$ , what is $f'(x)$ equal to?

$anx^{n-1}$

When differentiating $ax^n$ , what do you do with the power $n$ ?

Multiply with coefficient, subtract 1

What is the derivative of $f(x)=-2x^3$ ?

$-6x^2$

What is the derivative of $f(x)=7x$ ?

$7$

What is $f'(x)$ if $f(x)=-x^3+2x^2+3x+8$ ?

$-3x^2+4x+3$

What is the derivative of a constant?

$0$

Why is the derivative of $f(x)=3$ equal to $0$ ?

Rewrite as $3x^0$ , so $3(0)x^{-1}=0$

To differentiate $f(x)=\frac{1}{x}$ , what should you do first?

Rewrite as $x^{-1}$

What is the derivative of $f(x)=\frac{1}{x}$ in fraction form?

$-\frac{1}{x^2}$

Why is it bad practice to leave negative powers in answers?

Should convert to fraction form

What is the derivative of $f(x)=2\sqrt{x}$ in simplest form?

$\frac{1}{\sqrt{x}}$

Explore Leaving Cert Mathematics Revision Notes by Topics

The Basics

Curve Sketching

Implicit Differentiation

Rates of Change

Trig/Exponential Functions

Explore Leaving Cert Mathematics Model Answers by Topics

The Basics

Curve Sketching

Implicit Differentiation

Rates of Change

Trig/Exponential Functions

Explore Leaving Cert Mathematics Flashcards by Topics

The Basics

Curve Sketching

Implicit Differentiation

Rates of Change

Trig/Exponential Functions

Explore Leaving Cert Mathematics Exam Questions by Topics

The Basics

Curve Sketching

Implicit Differentiation

Rates of Change

Trig/Exponential Functions

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