00:01
The task is to find the derivative of this giant product 2x squared times a quantity of x cubed minus 3 to the fourth.
00:16
So as you heard me say, we have a giant product in here.
00:22
Right there is your product, which is telling us that we need to do the product rule.
00:27
We have the left side.
00:28
And if you look at the right side, you have this inner function and this outer function, which is telling us that we're going to do the chain rule when it comes time to do that.
00:39
So doing the product rule, you take the derivative of the left side, which is 4x, you leave the right side alone.
00:46
That's the quantity of x cubed minus 3 to the fourth power.
00:49
And plus now you leave the left side alone, and you take the derivative of the right side, which is where your chain rule happens, where you bring that 4 in front, and it's now to the third power.
01:01
You leave the xq minus 3 alone times the derivative.
01:06
Derivative of the inside 3x squared and i try to code for this to help you but then that might not be helpful and some teachers will let you leave your answer like this i know this is not simplified but i'll circle it because it's very tough for you know somebody like me to tell you what your teacher wants because you could just simplify by multiplication you can multiply all these terms together like two times four is eight times this three is 24, x to the fourth, x squared, x squared, you add the exponents, and you show that x cubed minus three to the third...