# Differentiation

A list of resources to support the teaching and learning of Differentiation in A level mathematics.

### Investigating Stationary Points and Finding the Value of the First Derivative at a Particular Point on the Curve

These videos from Casio explain how to use calculus to find the stationary points of the curve y = x/(16+x2) by rewriting the equation as a product using index form and using the product rule to find the differential. .

The second part of the explanation shows how to find the value of the differential of y= (1+e3x)5/3 at x = 1/3ln5 using the chain rule.

Graphical solution 1 explains how to use the graphic calculator to find the coordinates of the stationary points of the given function.

Graphical solution 2 explains how to use graphic calculator to find the derivative of the given function at the required value of x to verify the mathematical solution

### Find the Value of the First and Second Derivative of a Function in x, at Specified Values of x

These videos from Casio explain how to find the value of the first and second derivatives of a given function at specific values for x.

The graphical solution explains how to use the graphic calculator to find the derivatives at specific values of x in order to verify the solution.

### Differentiation

This RISP activity introduces the subject of differentiation.

Rather than start from first principles or learning a rule, the activity suggests using a graphing package to generate data.

Starting with a quadratic graph, students find the gradient of the curve using a straight line graph and are encouraged arrive at a rule for differentiating a power of x through pattern spotting.

### Differentiation Exercise

This interactive resource is designed to enable students to explore the differential function of a polynomial and conclude by forming a generalisation.

An instruction page explains to students that they should draw a polynomial. Then by sliding the slider the gradient of the curve is plotted, on the same axis, for a sequence of x-values. Students are then required to fit a curve to the plotted points hence finding the equation of the differential function.

Once the exercise has been repeated several times, in a strategic manner, students are expected to generalise their results.

### Differentiation

These resources cover aspects of differentiation which are suitable for students studying mathematics at A Level. Some of the topics covered include, differentiation from first principles, a table of common functions and their derivatives, the chain, product and quotient rules, as well as maxima and minima.

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of differentiation will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided

### Matching Functions and Derivatives C3

This resource requires students practise to differentiating quadratic functions and finding the values of a function and its derivative at specific points.

Students will distinguish between f(x) and f′(x), relate values of f(x) and f′(x) to the graph of y = f(x) and reflect on and discuss these processes.

Before starting this activity students should have some understanding of function notation and differentiation of quadratic functions.

### Differentiating and Integrating Fractional and Negative Powers C4

This resource requires students to convert functions into an appropriate form for differentiating or integrating and then differentiate and integrate negative and fractional powers of x.

Before starting the activity students should be able to differentiate and integrate polynomial functions and have some knowledge of fractional and negative indices.

### Basic Differentiation Refresher

This refresher resource for basic differentiationhas been designed to enable students to prepare for their university mathematics programme. There is a comprehensive review including differentiation of a general power multiplied by a constant, simple fractions and general brackets.

Although it has been produced for students about to enter university, it is also a very useful resource for those currently studying A Level Mathematics.