00:01
Okay, in this problem, we're finding the derivative of our function.
00:04
F, f of x equals 4x to the 5 fourths.
00:12
Oops, there you go.
00:14
And then plus 8x to the three halves, 8x to the three halves, and then plus 9x.
00:23
So we're going to use the power rule for each of these.
00:25
We're going to say f prime of x.
00:27
It's going to be equal to.
00:28
I'm going to bring my 5 fourths down and multiply it to 4x, and that's going to give me 5x.
00:32
Going to subtract 1.
00:33
That's going to be 5x to the 1 fourth.
00:36
Then i'm going to do the same thing with 8x to the 3 halves.
00:38
I'm going to bring down 3 halves and multiply it by 8.
00:41
So i'm going to divide by 2 and then multiply by 3.
00:43
It's going to give me 4 times 3, which is 12x.
00:46
And then i'm going to subtract 1, so that's going to be to the 1 half.
00:49
And then i'm going to say plus 9.
00:52
All right.
00:53
Now find the derivative of f of x equals, well, find each of the following.
01:02
All right, i'm going to do f prime of 1.
01:04
So f prime of 1 is going to be 4 times 1 to the 1 4th plus...