What is differentiation?

Differentiation is a way of measuring a rate of change. Formally, we can look at two points on a curve and as an example, I would use the x^2 curve. We can plot on a point (x,x^2) and a point (x+h, (x+h)^2). Then I would write the gradient of the line between the two points as a quotient and explain the limit as h tends to zero, explaining that this means we will find the gradient of the tangent of x^2 at that point. Then I would generalise the case for a function f(x).
We would then go through another example to see if they can spot the pattern of how differentiation works and finally I would explain the process of bringing down the power, and taking away one from the power index to form the new power. Finally, we can go through more questions.