Differentiate cosx from first principles

Incompetent

Where I'm stuck is here

So I can get down to when you divide by h. Then in the marking scheme it seems to only divide half of it by h? And then it halfs the top and bottom, and the sin disappears? It's clearly some rule I don't know about... . Anyone offer some assistance?

DepoProvera

You can 'take' the -2sin(x +h/2) out of the fraction as when you multiply something by a fraction it goes on the top, so you're just doing the reverse.


Then you multiply the whole thing by a half, which makes the -2 into -1 (they don't show the 1), and makes the bottom of the fraction h/2

Then it just uses the rule that sin(x)/(x)=1

unmoeglichkeit

You can just finish that by introducing a limit to both sides. The part on the left of the equal sign at the end is just another way of saying dy/dx.

DepoProvera

Hard to explain it typing so I wrote it out

Edit: fook beaten