00:01
So if we want to take the derivative of the function, y is equal to 1 over 3x squared minus 4 to the 5th power, recall that we were able to solve this when we were talking about the quotient rule in the last chapter, but what we can do instead, since we're working with chain rule right now, if we rewrite this to where it is a power, just a pure power, so 3x squared minus 4 all to the negative fifth power.
00:46
Negative fifth power.
00:50
Then you might see that this here is just the generalized power formula.
00:56
So if i let this inside function here, the h of x.
01:02
So i'll go write that off button to the side.
01:04
H of x is equal to 3x squared minus 4.
01:13
So i could rewrite y here as h of x to the negative fifth power.
01:31
So y prime is going to be, so first i'll just write d, d, the x of h of x to the negative fifth power.
01:49
And so since it's the generalized product formula, i'm sorry, power formula, i will go ahead, take the power, multiply it out front, and subtract the one from the power.
02:05
So i'll end up with negative 5 times h of x raised to the negative 6 power, and then i'll have to multiply by the derivative of 6th power, and then i'll have to multiply by the derivative of, h of x.
02:30
So all i need to do is figure out what h prime of x is.
02:33
Let's do that over here.
02:35
So h prime of x is equal to.
02:40
So remember the derivative i can distribute across plus and minus signs as well as pull any kind of constant past it...