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3## XLatest Additions

8193Differentiation : Trig functions : Visualise cos (x ± a) Addition Formulae

8192Differentiation : Trig functions : Visualise sin (x ± a) Addition Formulae

8057Differentiation : Slope : The graph of y = x³

8056Differentiation : Slope : Straight v curved

8050Differentiation : Slope : The graph of y = x²

8024Differentiation : Implicit differentiation : Exam Question

8013Differentiation : Implicit differentiation : Exam Question

8007Differentiation : Rules - the product rule : Exam Question

7996Differentiation : Related rates of change : Exam Question

7993Differentiation : Implicit differentiation : Exam Question

7991Differentiation : Trig functions : Exam Question

7990Differentiation : Rules - the quotient rule : Exam Question

7988Differentiation : e

^{x}: Exam Question7984Differentiation : Rules - the quotient rule : Exam Question

7983Differentiation : Ln x : Exam Question

Differentiation is used to find the gradient function (derivative) for a curve, the gradient at any point on a curve, and also to find the equation of the tangent or normal to a curve at a point on the curve. Differentiation, as part of calculus, is used in science and engineering, and was developed originally in the 17th century by Newton and Leibniz.

Investigate Cubics

Straight v curved

Investigate Quadratics

Investigate Higher Order Polynomials

Tangents and Chords

Introduction

The graph of y = x²

The graph of y = x³

Constant multiplier

Sums and differences

Investigate with Negative Powers

Gradient curves

O-test 1

O-test 5

Investigate

Approximate gradient

Randomized Exam Q 2009

Approximate gradient 2

Tangents and Chords of Polynomials

Function notation

Function notation 2

Function notation 3

Function notation 4

Function notation 5

Function notation 6

Delta notation

Differentiability

Differentiability 2

Differentiability 3

Differentiability 4

Randomized Exam Q 2008

Randomized Exam Q 2008

Investigate

Investigate 2

Problem 1

Problem 2

Problem 3

Problem 4

Rolle's Theorem

Rolle's Theorem 2

Rolle's Theorem 3

Rolle's Theorem 4

Randomized Exam Q 2009

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Assessment

Randomized Exam Q 2009

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Some 1st and 2nd Derivatives

Randomized Exam Q 2011

Differentiate x

^{n}Differentiate simple functions

Differentiate products

Differentiate quotients

Check the steps

Timed O-test

O-test 1

True or false O-test

Matching O-test

Sequence O-test 1

Sequence O-test 2

Matching O-test

Sequence O-test 3

Memorise the rules

Logical order

dy/dx = 1/dx/dy

Randomized Exam Q 2014

2nd order derivatives

2nd order derivatives 2

Verify dy/dx = 1/dx/dy

Randomized Exam Q 2005

True or false

2nd order derivatives 3

Spot the method

Randomized Exam Q 2005

Randomized Exam Q 2006

True or false 2

2nd order derivatives 4

Randomized Exam Q 2007

True or false 3

Matching O-test

Randomized Exam Q 2007

Randomized Exam Q 2000

Derivative puzzles

Randomized Exam Q 2003

Rational powers

Rational powers 2

Rational powers 3

Randomized Exam Q 2004

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O-test

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O-test 2

O-test 3

O-test 4

Exam O-test 1

Exam O-test 2

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam timed O-test

Randomized Exam Q 2014

Randomized Exam Q 2011

Exam O-test 1

Randomized Exam Q 2009

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Randomized Exam Q 2014

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Randomized Exam Q 2014

O-test 4

Finding tangents 2

The gradient curve

Tangents 1

Tangents 2

Tangents 3

Evaluating the gradient

Evaluating the gradient 2

Evaluating the gradient 3

Evaluating the gradient 4

Finding tangents 1

Finding tangents 3

Finding tangents 4

Finding tangents 5

Finding tangents 6

Randomized Exam Q 2002

Check the method

Randomized Exam Q 2004

Timed O-test

Randomized Exam Q 2004

O-test 1

Method O-test

Randomized Exam Q 2005

O-test 2

Randomized Exam Q 2006

Finding normals

Finding normals 2

Finding normals 3

Finding normals 4

Finding normals 5

Gradient on a GDC

Gradient on a GDC 2

Randomized Exam Q 2005

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Randomized Exam Q 2007

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Vocabulary O-test

O-test 3

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam O-test 5

Investigate 1st & 2nd Derivatives 2

Investigate 1st & 2nd Derivatives

Second order derivatives

Randomized Exam Q 2000

Randomized Exam Q 2007

Randomized Exam Q 2007

Exam O-test

Investigate Increasing Functions

Randomized Exam Q 2009

Randomized Exam Q 2010

Randomized Exam Q 2009

Randomized Exam Q 2009

Decreasing f(x) = 3 - 3 to x

Increasing f(x) = 2 to x + 1

Increasing f(x) = log(x)

Prove an increasing function

Prove an increasing function 2

Randomized Exam Q 2000

Decreasing f(x) = 1 - x - x to 3

A decreasing function 3

Increasing or Decreasing ?

Increasing and decreasing

Increasing and decreasing 2

Randomized Exam Q 2007

Randomized Exam Q 2008

Randomized Exam Q 2008

Exam O-test

Randomized Exam Q 2011

A minimising problem

Randomized Exam Q 2009

Randomized Exam Q 2010

View Maxima and Minima 2

Randomized Exam Q 2009

Randomized Exam Q 2010

O-test 3

The max-box problem 3

Finding turnings points

Randomized Exam Q 2010

A minimising problem 2

Randomized Exam Q 2009

Randomized Exam Q 2009

Randomized Exam Q 2011

View Maxima and Minima

The max-box problem 2

Randomized Exam Q 2009

Randomized Exam Q 2003

Randomized Exam Q 2009

Investigate Points of Inflection

Introduction

Maxima and minima

Axis of symmetry

Finding turnings points 2

Finding turnings points on a GDC

O-test 1

Finding turnings points 3

Method O-test

A maximising problem

Randomized Exam Q 2000

Randomized Exam Q 2000

A maximising problem 4

Randomized Exam Q 2001

The max-box problem

A minimising problem 3

A minimising problem 4

A minimising problem 5

Randomized Exam Q 2002

O-test 2

Randomized Exam Q 2007

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Quiz

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Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam timed O-test

Investigate Trig Differentiation

Randomized Exam Q 2009

Randomized Exam Q 2011

Randomized Exam Q 2010

Randomized Exam Q 2009

Finding tangents 2

Randomized Exam Q 2011

Finding tangents 1

Tangents and Chords of Trig Functions

Visualise cos (x ± a) Addition Formulae

Tangent and normal 2

Visualise sin (x ± a) Addition Formulae

sin x by first principles

More trig functions

cos x by first principles

sin kx

cos kx

Examples

Examples 2

Examples 3

Derivative puzzles

tan and cot

sec and cosec

True or false O-test

Finding tangents 3

Differentiation on a GDC

Randomized Exam Q 2004

Randomized Exam Q 2006

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Exam O-test 1

Exam O-test 2

Randomized Exam Q 2009

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Visualise the Product Rule

Investigate

The product rule

The product rule 2

The product rule 3

The product rule 4

The product rule 5

Finding gradients

Finding gradients 2

Finding gradients 3

Finding tangents

Finding normals

Randomized Exam Q 2007

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Sequence O-test

Exam O-test 1

Exam O-test 2

Exam O-test 3

Randomized Exam Q 2010

Randomized Exam Q 2011

Randomized Exam Q 2011

Finding gradients

Randomized Exam Q 2009

Randomized Exam Q 2011

Randomized Exam Q 2009

Visualise the Quotient Rule

Investigate

The quotient rule

The quotient rule 2

The quotient rule 3

Finding turning points

Randomized Exam Q 2004

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Exam O-test 1

Exam O-test 2

Exam O-test 3

Randomized Exam Q 2010

The chain rule

Randomized Exam Q 2009

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Explanation

Investigate the chain rule

Explanation 2

(ax+b)ⁿ

(ax+b)ⁿ 2

The chain rule 2

The chain rule 3

The chain rule 4

The chain rule 5

The chain rule 6

Finding gradients

Finding gradients 2

Matching O-test

Sequence O-test 1

Sequence O-test 2

Randomized Exam Q 2006

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Exam O-test 1

Exam O-test 2

Exam timed O-test

Randomized Exam Q 2009

Randomized Exam Q 2011

Randomized Exam Q 2010

Randomized Exam Q 2010

How to solve...

Example 1

A sand problem

Example 2

Example 3

Example 4

Expanding cube

An expanding stain

Filling a water tank

Hot air balloon

Circle

Randomized Exam Q 2006

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Randomized Exam Q 2014

Randomized Exam Q 2008

Randomized Exam Q 2008

Exam O-test 2

Exam O-test 1

Exam timed o-test

Approximating square roots

Approximating cube roots

Approximating powers

Trig approximations

Trig approximations 2

Small changes to a circle

Small changes to a sphere

Small changes to a cube

Small changes to a triangle

Small changes to a tank

Randomized Exam Q 2011

By first principles

Randomized Exam Q 2009

Randomized Exam Q 2010

Gradients of a

^{x}Gradients of a

^{x}and e^{x}Differentiation of e

^{x}Examples

Finding tangents

Randomized Exam Q 2000

Randomized Exam Q 2014

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Exam O-test 1

Randomized Exam Q 2009

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Exam O-test

Randomized Exam Q 2011

Gradients of ln ax

Investigate Differentiation of ln ax

By first principles

Differentiation of ln ax

ln (ax+b)

Differentiation of x

^{r}Randomized Exam Q 2000

Finding tangents

Randomized Exam Q 2003

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Randomized Exam Q 2004

Randomized Exam Q 2006

Randomized Exam Q 2007

Randomized Exam Q 2008

Investigate Log/Exp Differentiation Together

Examples

Matching O-test

Sequence O-test

Randomized Exam Q 2006

True or false

Randomized Exam Q 2006

Randomized Exam Q 2007

Randomized Exam Q 2008

Exam O-test

Randomized Exam Q 2009

Randomized Exam Q 2010

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Randomized Exam Q 2010

Assessment

Randomized Exam Q 2009

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Randomized Exam Q 2009

Randomized Exam Q 2011

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Randomized Exam Q 2009

Randomized Exam Q 2014

Finding tangents

Example 1

Example 2

Example 3

Example 4

Example 5

O-test

Example 6

Example 7

Other variables

Finding a gradient

Finding normals

Finding tangents 2

Finding normals 2

Randomized Exam Q 2003

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Randomized Exam Q 2014

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Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam timed O-test 1

Exam timed O-test 2

Randomized Exam Q 2011

Randomized Exam Q 2009

x

^{n}and n^{x}a

^{x}a

^{bx}Randomized Exam Q 2007

Randomized Exam Q 2007

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Exam O-test 2

Exam timed O-test

Simple d.e.s

Exponential growth

Gradient

Gradient 2

Gradient 3

Gradient 4

Gradient 5

Gradient 6

Leaking water tank

O-test

An expanding cube

Fish

Population

Newton's law of cooling

Randomized Exam Q 2008

Xtra 1

MIT video: differentation

MIT video: products,quotients

MIT video: limits

MIT video: chain rule

MIT video: implicit differentiation

MIT video: implicit differentiation 2

MIT video: limits

MIT video: exponentials & logs

Velocity & acceleration

Changing direction

Two particles

Illustration

Illustration 2

Investigate Motion Calculus

Observation O-test 1

Observation O-test 2

A cyclist

Velocity & acceleration 2

A ball

Distance travelled

Test tube

Bouncing ball

O-test 1

Using integration

Using integration 2

Two boats

Randomized Exam Q 2005

Randomized Exam Q 2006