00:02
Here we have a composite function, and we're going to start by identifying the inside function and outside function.
00:09
So your square root symbol is serving as a grouping symbol, and inside it we find our inside function, g of x.
00:15
That would be 2 minus e to the x.
00:18
And so the outside function would be the square root of that, so the square root of x.
00:23
And for the sake of differentiation, i like to call square root x, x to the one -half power.
00:28
That way i can use the power rule.
00:30
Okay, now it's time to find the derivative, do y, d, d, s.
00:34
So according to the chain rule, we start by finding the derivative of the outside function.
00:39
And i'm going to rewrite the function as y equals 2 minus e to the x to the one -half power.
00:46
So the derivative of the outside function would be using the power rule on the one -half power function...