Differentiate Sin^2(X) with respect to X

'With respect to X' means we will be differentiating all the X parts (To put it simply). First we show that the differential of Sin(X) is Cos(X), we can show this graphically using the whiteboard. Then we should know from previous lessons that the differential of X^2 is 2X (We can show this with the formal definition of a differential using diagrams as aids). We then combine these two rules using a substitution for Sin(X) = U, still differentiating with respect to X (not U). Several lines of working and explaining will lead to the answer of 2Cos(x)Sin(x).