Product Rule: Prove It!

Рет қаралды 717

Күн бұрын

The product rule for differentiation gives us a formula that tells us how to combine the derivatives of 2 functions to find the derivative of the product of those functions. Why does that formula work? Let's Prove It!
[Thumbnail of man pointing, credit: Malte Helmhold ]

Пікірлер: 5

@TeFurto777 19 күн бұрын

7:52 but you haven't proved that those 2 expressions do not diverge. The denominator makes that needed

@MathsLikeALegend 19 күн бұрын

You are right! I will admit, I could not think of a nice way of fully justifying it while still making it clear to people who are not yet used to dealing with limit notation much. That is the main reason I mentioned about not wanting to deal with diverging/infinite limits when I was defining the limit properties at the beginning. I was hoping nobody would notice though haha.

@TeFurto777 18 күн бұрын

@@MathsLikeALegend Oh I see. That makes sense lol

@YoungPhysicistsClub1729 20 күн бұрын

use logarithms and it's a 2 line proof done in 30 seconds

@MathsLikeALegend 20 күн бұрын

yes!!! I really enjoy that method of showing it too because it works out so neatly (and will probably make a video on that method at some point). However, I was just trying to show the proof without using implicit differentiation because students have not learnt that yet at the point when they first come across Product Rule.