Calculus – Techniques for Differentiation

Several high quality resources are available online to help you practise your differentiation.


The mathcentre site includes extensive resources. The quick reference leaflets which are available on numerous topics are very clearly written and succinct. There are also teach yourself booklets, revision booklets, videos and diagnostic tests.

Math Centre – Product Rule     Math Centre – Quotient Rule      MathCentre – Chain Rule

or for the resources structured as a course try Mathtutor

Plymouth University workbook

Calculus workbook from Plymouth University

Plymouth University have an excellent series of workbooks with examples and exercises, note the dropdown menus for each topic. Try this on the Product and Quotient Rules or this on The Chain Rule.
Note the use of colour to make the examples clear. The example illustrated shows the quotient rule being used to differentiate tan x (with respect to x).

You can always check your work on WolframAlpha: (More on WolframAlpha)

…or try Symbolab.

Integration – applets

If you are learning about integration, there are some excellent online resources to help you. You can of course check your work with WolframAlpha and note that if you ask for a definite integral WolframAlpha will also return a visual representation of the integral, illustrating the area found. This is particularly helpful where parts of the curve are above the x axis and parts below. (You can see further calculus examples as part of Slideshow 4 on the WolframAlpha page).

Using the Integral Machine from The Center for technology and Teacher Education, University of Virginia, you can study approximate methods of integration such as the Trapezium Rule, try increasing the number of strips used and note how the area found using the Trapezium Rule (called Trapezoid here) gets closer to the actual area. You can also see from the shape of the curve why the trapezium rule can give an over or underestimate. Experiment with the four functions given.

Numerical Integration – Zweigmedia

If you use the Numerical integration utility and grapher from zweigmedia’s Finite mathematics and Applied Calculus you can choose your own function, then compare the actual value of the integral with that found by various approximate methods.

For some notes and examples on Integration, you could use resources such as The Math Centre or Just The Maths (starting at Unit 12.1).