Differentiation

Section overview:

The PowerPoint below provides an overview of material in this topic, including explanations and examples - for the full experience, open in a new tab then download it. All exercise references are to the new specification Pearson textbook - you can access the digital version for free or buy your own for extra practice. 

Written summary notes are also given below for quick revision of key points, plus a selection of exam-style questions (with solutions) to test your understanding.

P2-Chp9-Differentiation.pptx

Explore further:

The Lotka-Volterra differential equations model the populations of predators and their prey in mathematical biology. 

See more applications of differential equation in the video at the bottom of the page (hint: they're very important!).

Extra resources:

Use the videos below to support your understanding of the topic. The ones on the left are specific to the course, building up to demos of exam-style questions; the ones on the right are for your own amusement, although the alternative outlook may provide you with a deeper overall understanding and appreciation of the topic.

In particular, 'The Essence of Calculus' video series is dotted throughout the relevant topic pages in A-level Maths and Further Maths, or you can find the full playlist here. These videos demonstrate a deeper cut of some of the most important ideas within A-level, so they are well worth a watch!

The playlists below contain all A level differentiation content, some of which is repeated from the Y12 Differentiation page.

Playlist 1 - First principles, derivative graphs and concavity

Playlist 2 - Differentiating standard functions

Playlist 3 - Applications of differentiation

Playlist 4 - Chain, product and quotient rules and their applications

Playlist 5 - Implicit differentiation

Playlist 6 - Forming differential equations (see Y13 Integration for solving)

Extra fun! The Essence of Calculus - Geometric rates of change (now including trigonometric functions, extended from Y12: Differentiation):

The Essence of Calculus - Visualising the chain rule and product rule:

The Essence of Calculus - Exponential derivatives and e:

The Essence of Calculus - Implicit differentiation:

Here's that video on differential equations I was talking about at the top of the page! 

Working calculus around the real numbers (or is that the other way round?):