00:01
So if i want to find the derivative of f of x is equal to negative 7 times 3x to the 4th plus 2 all to the negative 4th power, then i may notice that i have to apply chain rule since i have a function 3x4 plus 2 inside of another function negative 7x to the negative 4th.
00:31
So i'll first go ahead and write this here as h of x, and i'll go and put that on to the side.
00:39
So i have h of x is equal to 3x to the 4th plus 2, and i'll go ahead and rewrite f of x as negative 7.
00:59
I'll put some parentheses here to the negative 4th, and then replace.
01:04
Place that with h of x.
01:09
So now if i want to take the derivative of this function here, so i end up with, so f prime of x is equal to the derivative of negative 7 or x, i was sorry, negative 7 h of x to the negative 4th power.
01:44
So i can go ahead and pull the scalar here or the constant out, negative 7, d, d x of h of x, to the negative fourth power.
02:13
So i'll need to apply power rule here.
02:18
So i move the negative 4 out front.
02:23
I subtract 1 from it.
02:27
So this would be, so negative 7 times negative 4 gives me 28, and then i'll have h of x raised to the negative 5th power.
02:52
And since i have a function within a function, i have to apply the chain rule.
02:56
So i'd end up with h prime of x on the outside.
03:04
So let's go over here and find what h prime of x is.
03:10
So i have h prime of x is equal to, so the derivative of 3x to the 4th plus 2.
03:28
So i can go ahead and distribute the derivative across the plus side as well as pull scalers out, since this is a linear operator...