00:01
So this is an excellent problem to get you to realize that you have a chain rule because something is being cubed.
00:10
That's going to be your outer function.
00:13
But your inner function, the thing that's inside the parentheses, is a quotient rule.
00:21
I'll just write is a quotient because when you get to doing that problem, you have to do the quotient rule.
00:27
So we have 3t plus 4 over 16 minus 7.
00:35
So the way i would do this problem, and i would probably stop once i do this, is i would take the derivative of the outer function.
00:42
I would be your power rule where you move that 3 in front, and then you subtract 1 from the exponent.
00:48
And what you do for the chain rule is you leave the inner function alone.
00:55
And then what you have to do is multiply by the derivative of the inner function, which again is a quotient, so it's a quotient rule, where you take the derivative of the top, you'll leave the bottom alone minus the derivative of the bottom, leaving the top alone all over the denominator, 16 minus 7 squared.
01:18
So, well, i could probably simplify a little bit.
01:23
I'm not going to spend a lot of time simplifying because i think you can tell that what we definitely have in the numerator would be the, 3 and a 3 t plus 4 squared...