 In this video, we provide the solution to question number 10 for practice exam number 3 for math 1210, in which case we're given the function f of x is equal to the natural log of 1 plus e to the 2x power, and we're asked to find f prime at 0. So we first need to compute the derivative. So what is f prime? Notice that the chain rule is in play here. We have the function 1 plus e to the 2x inside of the natural log, like so. So by the chain rule, we see the derivative is going to look like 1 plus e to the 2x on the bottom, and in the numerator, we get 1 plus e to the 2x prime. So we have to take the derivative of the top. Well, the derivative of a constant is equal to 0, and then another chain rule comes into play here. You have 2x inside of the natural exponential. And so applying the chain rule in that situation, you see the derivative will be 2 times e to the 2x, and this sits above 1 plus e to the 2x. This is our derivative. Now you'll notice that's not there because we're not looking for the derivative. We need to know the derivative at x equals 0. So if we plug in 0 to find the number we're looking for, we get 2 times e to the 0 over 1 plus e to the 0. e to the 0 is 1, so we get 2 over 1 plus 1, which is 2 over 2, which gives us 1. So we see the correct answer is f, number 1.