00:01
We'd like to differentiate f of x equals x squared from first principles.
00:04
The way i'm interpreting that is to say the limit definition.
00:07
We have limit as h approaches zero, f of x plus h minus f of x divided by h.
00:16
That is the slope of a secant line with a change in x of h.
00:22
And then we take the limit as h goes to zero.
00:25
So that's going to be the limit as h approaches zero, x plus h squared minus x squared divided by h, just substituting our value for f, our expression for the function f.
00:40
Let's go ahead and expand this out.
00:42
Take the limit of this is x squared plus 2 times x times h plus h squared minus x squared all divided by h.
00:51
X squared minus x squared cancel out.
00:54
We get the limit as h approaches zero, 2xh plus h squared over h.
01:01
We can cancel out these h's.
01:04
And we're going to get the limit as h approaches zero of 2x plus h...