00:01
Okay, here we have y equals e to the 5x.
00:03
I want to find dy by dx.
00:07
Well, the shortcut method is simply write down the exact same thing, e to the 5x, and then differentiate that and put it in front.
00:21
So 5x becomes 5, so the answer is 5e to the 5x.
00:28
And why is that? well, it's the chain rule.
00:31
So proof of that.
00:35
I would let u equal 5x.
00:41
So this item here, call it u, which means du by dx, is 5.
00:49
And then also we have y equals e to the u now, which means dy by du is also into the u.
01:00
I combine these together by the chain rule...