Leaving Cert Differential Calculus Set A Questions - L.C. Maths

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Algebra 1

0/14

Algebraic Fractions

Binomial Expansions

Algebraic Identities

Linear Equations

Simultaneous Linear Equations

Algebra 2

0/16

Quadratic Equations

Quadratic Roots

Simultaneous Linear & Quadratic Equations

Forming Quadratic Equations

Maxima and Minima

Polynomial Graphs

Trigonometry 1

0/18

Sine, Cosine & Tangent

The Unit Circle

Trigonometric Graphs

Related Trigonometric Graphs

Solving Trigonometric Equations

Coordinate Geometry of the Line

0/14

Area of a Triangle

Equation of a Line

Dividing a Line Segment

Triangle Concurrencies

Distance from Point to Line

Angle between Lines

Real World Problems

Probability 1

0/14

Elementary Probability

Relative Frequencies

Mutually Exclusive Events

Independent Events

Conditional Probability

Geometry 1

0/6

Triangle & Parallelogram Theorems

Circle Theorems

Differential Calculus

0/10

Derivatives from First Principles

Derivatives by Rule

Product, Quotient & Chain Rules

Second Derivatives

Trigonometry 2

0/10

Trigonometric Identities

Compound Angles

Double-Angle Formulae

Sum, Difference & Product Formulae

Inverse Trigonometric Functions

Sequences & Series

0/12

Arithmetic Sequences

Arithmetic Series

Geometric Sequences

Geometric Series

Limits of Sequences

Other Sequences

Statistics 1

0/9

Population Sampling

Location & Variability

Stem & Leaf Diagrams

Distribution Shapes

Coordinate Geometry of the Circle

0/14

Circles centred at Origin

Circle centred Elsewhere

Finding Equations of Circles

Touching Circles

Circles Tangent to Axes

Algebra 3

0/16

Quadratic & Rational Inequalities

Mathematical Proofs

Exponential Functions

Logarithmic Functions

Proofs by Induction

Complex Numbers

0/12

Introduction to Complex Numbers

Manipulating Complex Numbers

Conjugate Roots Theorem

Polar Coordinates

Argand Diagrams

De Moivre’s Theorem

Geometry 2

0/4

Integration

0/8

Indefinite Integrals

Definite Integrals

Integration & Areas

Average Values of a Function

Differential Calculus Applications

0/8

Stationary Points

Graphs of Derivatives

Maxima and Minima Problems

Rates of Change

Financial Maths

0/8

Compound Interest

Loans & Mortgages

Length, Area & Volume

0/6

Sectors of Circles

Trapezoidal Rule

Probability 2

0/9

Expected Values

Bernoulli Trials

The Independence of Events

Functions

0/15

Set Representation of Relations

Graphical Representation of Relations

Graphing Similar Relations

Introduction to Functions

Inverses & Compositions

Types of Functions

Exponential Functions

Logarithmic Functions

Functions & Graphs

Statistics 2

0/4

Scatter Diagrams

Lines of Best Fit

Normal Distributions

Inferential Statistics

0/6

Population Proportions

Central Limit Theorem

Population Means

Digital Lessons

About Lesson

Start with the quiz…

Knowledge Check Quiz

EXAMS.IE

Derivatives & Slopes

Hint

The derivative of \(x^n\) is \(nx^{n-1}\).

1 / 5

If \(y=x^2\), what is \(\dfrac{dy}{dx}\)?

\(x\)

\(2x\)

\(x^2\)

\(2x^2\)

The derivative of \(x^n\) is \(nx^{n-1}\).

That's right!

The derivative of \(x^n\) is \(nx^{n-1}\).

Hint

The derivative of \(a^x\) is \(a^x\ln a\).

2 / 5

If \(y=2^x\), what is \(\dfrac{dy}{dx}\)?

\(x(2^x)\)

\(2^{x-1}\)

\(2^x\ln2\)

\(\ln(x-1)\)

The derivative of \(a^x\) is \(a^x\ln a\).

That's right!

The derivative of \(a^x\) is \(a^x\ln a\).

Hint

The derivative of \(x^n\) is \(nx^{n-1}\).

3 / 5

If \(y=\dfrac{1}{x}\), what is \(\dfrac{dy}{dx}\)?

\(\ln x\)

\(\dfrac{1}{x^2}\)

\(\ln\left(dfrac{1}{x}\right)\)

\(-dfrac{1}{x^2}\)

The derivative of \(x^n\) is \(nx^{n-1}\).

That's right!

The derivative of \(x^n\) is \(nx^{n-1}\).

Hint

The derivative of \(e^{ax}\) is \(ae^{ax}\).

4 / 5

If \(y=e^{-2x}\), what is \(\dfrac{dy}{dx}\)?

\(e^{-2x}\)

\(e^{2x}\)

\(2e^{2x}\)

\(-2e^{-2x}\)

The derivative of \(e^{ax}\) is \(ae^{ax}\).

That's right!

The derivative of \(e^{ax}\) is \(ae^{ax}\).

Hint

The derivative of \(e^{ax}\) is \(ae^{ax}\).

5 / 5

For which of the following functions is \(y(x)=y'(x)\)?

\(e^x\)

\(\ln x\)

\(\dfrac{1}{x}\)

\(x\)

The derivative of \(e^{ax}\) is \(ae^{ax}\).

That's right!

The derivative of \(e^{ax}\) is \(ae^{ax}\).

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