00:01
All right, let's go ahead and do this problem.
00:04
So we are given an integral and we're supposed to find the derivative of this expression with respect to x using part one of the fundamental theorem of calculus.
00:16
So to do a real quick recap, it basically boils down to the fact that taking the derivative of an integral basically undo each other.
00:31
So if you have an expression that looks like this, what i want you to see that the variable used for the integration part is t, but you're plugging in an x.
00:44
This makes it into a function of x, as you can see over here.
00:50
So it's just that the relationship between large f and small f right here is that small f is the derivative of large f, or you could also say that the anti -derivative or the integral of small f is large f okay so if you take the derivative of large f of x it just ends up being small f of x so from the point of view from here what it looks like it just seems like the integrand and the d t just disappeared and instead of a t now you have an x okay, so this is the most straightforward way that you would do this problem.
01:38
So you would have to still deal with situations, situations such as the product rule, the quotient rule, the chain rule, because you're still taking a derivative...