I have a Calculus questions

[Ydoow]

I took a quiz and got a 23/25 on it.

Yay.

So, the question part is how I got near full credit (8/10pts) on the first question, when this was the equation I was left with

(deals with implicit differentiation)

e^y(cos(x)) = xy` + y -y`sin(x)

then I had to make the equation equal to y` (the ` means derivative of)

I wrote this

e^y(cos(x))-y / x+sin(x) = y`

and it was correct to this

e^y(cos(x))-y / x-sin(x) e^y = y`

So here are my questions

1.) I understand that the + should have been a -, but where the deuce did the e^y come from?

2.) I was pretty confident (while taking the quiz) that what I had before I equated it to y\', could not truly become equal to y`

I thought it would end up with ... = y`-y` which would not make sense at all. Basically I just said 'Welp...I know what it should look like...' and wrote it out like that, completely disregarding any algebraic rules. lol.

So did I just totally luck out and this actually makes sense? Or did the grader screw up and my process really is funked up?

[UmbralRaptor]

No idea where the second e^y came from. As for getting the y` by itself:

Getting to this should be self-explanatory:

e^y(cos(x)) - y = xy` - y`sin(x)

Now factor out the common term...

e^y(cos(x)) - y = (x - sin(x))y`

...And divide.

(e^y(cos(x)) - y) / (x - sin(x)) = y`

[Ydoow]

*facepalm*

That\'s like my favorite thing to do, factoring out numbers like that.

I\'m not entirely surprised I missed that on the quiz, I barely finished on time.

But I should have seen that when I reviewed it earlier today.

Thanks, that really cleared up my issues. Except for that e^y...I think she just made a mistake