====== Understanding Differentiation ====== ===== Introduction ===== This article assumes that you are familiar with straight line graphs, the idea that a line has a gradient and that a gradient represents a rate of change. You also need to understand how use algebra and how to manipulate algebraic equations. If you are happy then read on... ===== Zooming In On A Curve ===== The diagram below shows the graph of the function y=x^3 We are asked the question: how do we find the slope, otherwise known as the //rate of change//, of the graph at a particular value of x? ===== Exercises ===== Find the derivative (the gradient function) of the following (the first one has been done for you)... 1) y=x^2+1 **ANSWER:** \frac{dy}{dx}=2x 2) y=2x^2+3x+1\\ 3) y=x^5+12\\ 4) y=2x^4-3x^3+x^2-3x+1\\ 5) y=10x^4+3x^2+12\\ 6) y=x^{-4}+1\\ 7) y=-5x^{-2}+3x^2\\ 8) y=x^{-3}-3x^{-2}\\ 9) y=-x^{-1}+2\\ 10) y=-5x^2+5x^2+100