00:05
If f of x is equal to the square root of x, and if a is the number 9, then using the definition, the limit definition of the derivative, f prime at a would be, let me erase that, i've got to put in the word limit, f prime of a would be the limit as h approaches zero of the function evaluated at x plus h minus the function evaluated at x over h and actually instead of x since we're evaluating the derivative at a instead of x we're going to put a so f prime of a will be the limit as h approach is zero of the function at a plus h minus the function of f at a over h now using uh this definition for the function f of x is to square root of x and our number a is nine uh i'll continue down here uh this will equal the limit as h approaches 0.
02:00
Now, the function f of a plus h is going to be the square root of a plus h, minus the function at a.
02:18
F of x is square root of x, so f of a is a square root of a.
02:24
All of this is divided by h.
02:27
And we're taking the limit of this expression as h goes towards zero.
02:31
That's how we're going to find f prime of a.
02:39
Keep in mind, let's scroll up just a minute so you remember...