A level maths: differentiation

[Uninspirednamewise]

DS (Year 12) has been revising the topic of differentiation for his A level maths today, but finding it hard to understand. Does anyone know of any good resources that explain this clearly at the right level for an A level student? (Board is OCR if that makes a difference.)

What exactly is he finding hard to understand? Are you talking about from first principles or just the whole concept.

Pictorially it's getting the gradient of a graph at any one point.

To find the gradient of a point at GCSE you draw a line just touching the curve (tangent) hopefully it will be approximately the same angle as the curve.
You then work out the gradient by taking the change in the y co-ordinates and dividing by the change in x co-ordinates.

For differentiation (from first principles) you work on the idea that you look at a tiny tiny change in the x coordinates. You call the tiny change dx. You then do the same as working out the tangent gradient-change in y divided by change in x.
Then you look what happens as you make the tiny change dx smaller and smaller. (we call it approaches 0)

It is something fairly necessary for A-level maths (and he'll need it for physics too if he's doing it). If he really is struggling to understand it then I suggest he asks a teacher for a session where they can really talk it through.

He can probably get quite a long way by just learning the rules and when you apply them. So y=xn: dy/dx = nx(n-1) for all n is constant (even irrational) is the basic one, but there are other ones that he'll need to learn.

I like this guy:
www.examsolutions.net/pure-maths-help/
Look for 'Differentiation 1'

nrich.maths.org/4722

Your son needs to get this topic learnt and understood. A great deal of A level content depends on it, without a decent grasp of differentiation he will really struggle.

Thank you very much for your replies. I only did maths to O level, so have no knowledge of differentiation (other than what I have now picked up from the 2 replies above ). So I don't really know how much DS does or doesn't understand. DS is not doing physics A level, but is doing chemistry. Is differentiation also required for chemistry?

Anyway, what I have definitely understood from your responses is that this is a key topic which forms the foundation for other topics, so I have decided to get DS some private tuition. DS's results to date have been a strange mix - he has had the full range of grades in his topic tests!

CGP revision guides are excellent. Also I found a resource on the net some years ago which provided a proof for differentiation by taking the gap from some small amount down to zero, but have looked and cannot fid it again. Dd found it useful to see "why" differentiation worked.