One application of derivatives from first year calculus is something called differentials. The intent is to find the change of something based on the derivative of a function and some sort of varialbe like time or a distance or something. Let's say you have this formula: y = x^2 now here is the derivative: dy/dx = 2x now if you bring the dx over, it looks like this dy = 2x dx In math class, these are meant to find changes in things. Let's say you wanted to find the change in y when x changes from 5 to 10. you would just fill in the equation like this: dy = 2(5)(5) dy = 50 the dy is your change in y. the first 5 is your original x value. the second 5 is your change in x. The differential said the change is 50. Now lets see what the original equation says the difference is: final - original = x^2 - x^2 = 10^2 - 5^2 = 100 - 25 = 75 The two different equations give VERY different answers. They're not even close. Knowing this, why do we still learn these?