00:01
So you're given the function y equals 2x minus 5 to the negative 1 power, and then x squared minus 5x to the 6th power.
00:12
We can write that as x squared minus 5x to the 6th power over, and we can have 2x minus 5x.
00:23
And which way will be easier to simplify? i, you know, i don't know.
00:28
But let's find what y prime is or dydx.
00:32
And so i'll use the quotient rule.
00:35
So we have the denominator times the derivative of the numerator, and the numerator will be six times x squared minus 5x to the fifth power, times the derivative of the inside, and the inside of this is 2x minus 5.
00:55
And then we have minus.
00:58
So we have the denominator times the derivative of the numerator.
01:03
And the numerator we had to use the chain rule.
01:06
And then the numerator, x squared minus 5x to the 6th power, times the derivative of the denominator, which is this two, all over the denominator squared.
01:23
So whether you have to simplify this or not, i don't know.
01:27
But if i write this out, we'll do this in a couple steps.
01:32
We would have a 2x minus 5 quantity squared times an x squared minus 5x to the fifth power minus 2 times this x squared minus 5x to the 6th power all over this 2x minus 5 squared.
01:53
Now we do have a common factor right here.
02:02
Of that and right here.
02:06
So we can factor out of the top and end up having two.
02:13
Let me go back to black.
02:15
Have two times...