OK, my illustrious, math-proficient readers, here is your first challenge!
Before you learn how to do derivaties in the normal way, you calculate them using limits. The general formula looks like this:If you try this for, for instance, f(x) = x^2, you'll see you can pretty easily get to f'(x) = 2x. (The general trick, if this all looks completely unfamiliar, is to somehow massage the formula until it's solvable with h = 0.)
The one I couldn't solve was the one where f(x) = sqrt(1 + 2x). The formula for the limit looks like this: