what does 'differentiation' mean?
Differentiation at A level is a method of working out the gradient of curves that aren't straight lines. If you have a function that is non-linear, which means any function that isn't in the form y= mx + c, the gradient of the curve will change at every point on the graph. This means you can only work out the gradient of the curve at specific points on the graph. Differentiation gives us a formula for calculating the gradient at any specific point. For example, if you want to work out the the gradient of the curve on the graph y=x2, then you can use differentiation to work out the gradient function, which in this case is dy/dx=2xOnce we have this formula, we can calculate the gradient at specific point on the graph - say (3,9) At this point x=3 so if you plug in 3 to the gradient function you get 2(3)=6. So, when you differentiate a function, you get a formula resulting from that function called the gradient function, and if you plug in a value of x into the formula you achieve the gradient of the curve at that point on the original curve.
