Calculus Comic-Connor Callahan
Storyboard Text
- Hey, Bradley before class starts do you think you could help me understand how product rule works?
- Sure Cynthia I would love to help you get a better grasp of product rule.
- First thing, product rule is used to find the derivative of an function, product rule states the derivative of the product of two functions is equal to the first function multiplied by the derivative of the second function plus the second function multiplied by the derivative of the first function.
- So if we have the function F(x)=(x-2)(x+3), we would take the first function which is (x-2), and multiply it by the derivative of the second function which would be (x+3) and that derivative is 1, so we would have (x-2)(1), then we would add it to the second function (x+3) multiplied by the derivative of the first function (x-2) which the derivative would be 1, so for the second half, we have (x+3)(1).Altogether we have (x-2)(1)+(x+3)(1)F'(x)=(x-2)+(x+3) which equals 2x+1OHHHH, okay I understand how product rule works thank you so much Bradley. Let me try one on my own.
- Okay, so if I wanted to take the derivative of the function F(x)=(x^2 +3)(x+2), I would start by multiplying (x^2 +3) with the derivative of the second function which is (x+2) and the derivative is (1), so the first half would be (x^2+3)(1), then add the second half which is the second function, (x+2) multiplied by the derivative of the first function which is (x^2 +3) and the derivative of that is (2x), so for the second half I would have (x+2)(2x)Altogether I would have F'(x)=(x^2+3)(1)+(x+2)(2x)which is F'(x)=3x^2+4x+3.Wow, Cynthia you really caught on quickly, that's a great job using product rule.
- Time for class, everyone please get seated, and take out your notebooks, today we will continue product rule.
- I just want to thank you so much.Oh well it looks like it's time for class, if we use product rule today I will be on top of it.
Over 30 Million Storyboards Created