00:01
Given that capital f is defined as x times the lowercase of x plus x times the lowercase of g.
00:12
And the fact that they ask for the second derivative, it makes sense to, at least in my mind, to find the first derivative because the derivative of the derivative is the second derivative.
00:24
So what you need to identify is that you have product rules happening in here, where you leave alone, take the derivative plus take the derivative and the derivative of x is one and then leave alone.
00:41
And then that plus is still there, but then you have another product rule right here where you leave alone, take the derivative, plus now you take the derivative of x, which is one, and then you leave g alone multiplication.
00:57
And then you just do it again, where you take the product rule, you leave alone.
01:03
Take the derivative, plus take the derivative, leave alone.
01:11
Then when you go to take the derivative of this, it's just f prime of x...