Differentiating Expressions (Leaving Cert Mathematics): Flashcards

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Differentiating Expressions
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What does differentiation measure?

Rate of change of a function

What does a derivative represent?

Slope of function's graph at a point

Derivative notation for f(x)f(x)

f′(x)f'(x)

Differentiate f(x)=axnf(x)=ax^n

f′(x)=anxn−1f'(x)=anx^{n-1}

Steps to differentiate axnax^n

Multiply power by coeff., subtract 1 from power

Derivative of a constant

00

How to differentiate polynomials with multiple terms?

Differentiate each term separately

Strategy for differentiating 1x\frac{1}{x} type expressions

Rewrite in index form

Best practice for negative powers in answer

Convert to fraction form

Strategy for differentiating sqrtxsqrt{x} expressions

Rewrite as power x1/2x^{1/2} first

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 Quizzes 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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