What is differentiation and what can it tell me?
Differentiation is something you can do to a function, to tell you about the gradient of the function. For your simple linear, quadratic, cubic, etc. equations, the process is the same every single time. You multiply the power by the factor to get the new factor, an you take 1 from the power to get the new power. The way you express an equation after you differentiate it is this dy/dx.Example:y = x2 + 3xdy/dx = 2x + 3Differentiation tells you the about the gradient of the function. The gradient of a curve at a given point on the curve is the gradient of the tangent to the curve at that point. For the example above, say you wanted to know the gradient at (1,4), you would simply put x = 1, into the function dy/dx. dy/dx for x = 1 2(1) + 3 = 5 The gradient of y = x2 + 3x at (1,4) is 5Knowing the gradient of graphs at any given point is a very powerful tool, and will be very useful to you going forward.
