00:01
Okay, this question wants us to find this derivative.
00:05
And to start, notice that if we try to take a derivative, we have a product here.
00:12
So we're going to have to use the product rule.
00:16
So for the product rule, it's derivative of the first.
00:21
So we're going to have to use the chain rule in this term.
00:23
So bring down the four, keep the inside alone, decrease the power by one, and multiply by the derivative of the inside.
00:34
And then we copy down the second term, leaving it unchanged.
00:40
And then for the second term of the product rule, we keep the first term the same, and then multiply by the derivative of the second term.
00:53
And this time, it's 5 times x squared plus x plus 1 raised to the 4th, times the derivative of the inside of that, which is 2x plus 1.
01:08
So now, let's simplify this a little bit...