 In this video, we will compute the solution to question number seven for practice exam number three for math 1210, we're asked to find the derivative of the function three to the x squared. So I want you to recognize that this is a composition of two functions. We have x squared as our inner function and we have three to the u as our outer function. And factor that out necessarily, I mean, do it if you need to, you get e to the u, right? Composed with this x squared and we're trying to take the derivative of these functions. So by the chain rule, when we calculate the derivative, we have to take the derivative of the outer function first. That's this exponential function e to the u for which the derivative, when you take the derivative of an exponential, you're gonna have to pay the tariff. So you get the natural log of three. You'll times that by three to the power x squared will be the power. So you have to put the inner function inside of the outer derivative and then you need to multiply that by the inner derivative. So we have to take the derivative of x squared, which we know the derivative of x squared is just gonna be a two x like so. So when you put that together, we see that the correct answer would be two times or two x times the natural log of three times e or three to the x squared. So we see that the correct answer is d. Let me briefly talk about some of these, some of these distractors here. So thumb some things to note, when you look at choice e, which is incorrect, it's because we didn't put the inner function inside of the outer derivative. That's a common mistake. Watch out for that. If you look at choice f, choice f, it has the outer derivative, but it doesn't have the inner derivative. That's also a very common mistake. So watch out for that. Some of the others are even worse, things like that, like, well, I mean, maybe not worse, but like choice a, you forgot to pay the tariff. So that's what's wrong with that. And then C and B are just combinations of some of those three common mistakes there. So do watch out. These multiple choice questions have the advantage that the solution is provided, but it also has the disadvantage that predictable common mistakes will also be included. So you have to double check your work to make sure you don't fall inside of those traps.