Easy derivatives are indeed easy - easier than that site makes them seem! We can approximate the slope (derivative) of any function y = f(x), at (x,y) as the s

Easy derivatives are indeed easy - easier than that site makes them seem! We can approximate the slope (derivative) of any function y = f(x), at (x,y) as the slope of a straight line from (x,y) to another nearby point (x',y') where y' = f(x'). The slope of this line is (y'-y)/(x'-x). Since we need x' close to x to make this accurate, we use x' = x + dx where dx is small, and we can also represent y' as y' = y + dy. So, then our slope is (y'-y)/(x'-x) = dy/dx = (f(x+dx)-f(x))/dx And that's all there is to it. e.g. For f(x) = x^2 dy/dx = ((x+dx)^2-x^2)/dx = 2x + dx We get the true value of the slope at (x,y) in the limit of dx -> 0, giving us the derivative of f(x) = x^2 as f'(x) = 2x.