/sci/ - Science & Math

i'm gonna bump this. Thinking of leaving my answer as it is, and just taking a points hit.

<span class="math">\frac{d}{dx} y^2 = \frac{d}{dx} xy[/spoiler]
<span class="math">2yy' = (cos xy)(xy' + y)[/spoiler]

And then a miracle occurs? I... don't know where you can go from there.

sin(xy) or sin(x)*y ?

>>1958414
Oh, well I guess you could always just leave it in terms of x and y.

<span class="math">2yy' = (cos xy)(xy' + y)[/spoiler]
<span class="math">2yy' - xy'(cos xy) = y(cos xy)[/spoiler]
<span class="math">y' = \displaystyle\frac{y(cos xy)}{2y - x(cos xy)}[/spoiler]

>>1958406
But you only have so many hit points, and the nearest Pokémon center is miles away.

ah, yeah, I totally missed the y². Not thinking clearly. The left side should be 2y(dy/dx) (I fucking hate that Leibniz notation, I much prefer prime notation, but what does the instructor use?)


y' = ((cos xy) * (xy' + y))/2y

I dunno how to get rid of the y' in the answer, that can't be right..

Also, how do you make your equations all fancy like that?

>>1958424
On the left you missed y'-y' didn't you? that's what I kept running into, they cancel out, unless I'm doing it way wrong.

>>1958416
Bro there's no parenthesis, it's just "sin xy" written exactly like that.

>>1958451
I "made it all fancy" with LaTeX.

Here's how you get the answer:

<span class="math">\displaystyle\frac{d}{dx} y^2 = 2y \displaystyle\frac{dy}{dx}[/spoiler]
<span class="math">\displaystyle\frac{d}{dx} \sin (xy) = (\cos (xy))(x\displaystyle\frac{dy}{dx} + y)[/spoiler]

Group the dy/dx's on the left side

<span class="math">2y \displaystyle\frac{dy}{dx} = (\cos (xy))(x\displaystyle\frac{dy}{dx} + y)[/spoiler]
<span class="math">2y \displaystyle\frac{dy}{dx} - x(\cos (xy))\displaystyle\frac{dy}{dx} = y(\cos (xy))[/spoiler]
<span class="math">(2y - x(\cos (xy))) \displaystyle\frac{dy}{dx} = y(\cos (xy))[/spoiler]
<span class="math">\displaystyle\frac{dy}{dx} = \displaystyle\frac{y(\cos (xy))}{2y - x(\cox (xy))}[/spoiler]

Hope I didn't make a LaTeX mistake there.

And of course, I did. Here you go.

<span class="math">\displaystyle\frac{dy}{dx} = \displaystyle\frac{y(\cos (xy))}{2y - x(\cos (xy))}[/spoiler]

(consolidating and testing math tags)
ah, yeah, I totally missed the <span class="math">y^2[/spoiler]. Not thinking clearly.

The left side should be <span class="math">2y\frac{dy}{dx}[/spoiler] (I fucking hate that Leibniz notation, I much prefer prime notation, but what does the instructor use?)

<span class="math">y'=\frac{(cosxy)*(xy' + y)}{2y}[/spoiler]

I dunno how to get rid of the y' in the answer, that can't be right..


>>1958424
On the left you missed <span class="math">y'-y'[/spoiler] didn't you? that's what I kept running into, they cancel out, unless I'm doing it way wrong.

>>1958416
Bro there's no parenthesis, it's just "sin xy" written exactly like that.

(consolidating and testing math tags)
ah, yeah, I totally missed the <span class="math">y^2[/spoiler]. Not thinking clearly.

The left side should be <span class="math">2y\displaystyle\frac{dy}{dx}[/spoiler] (I fucking hate that Leibniz notation, I much prefer prime notation, but what does the instructor use?)

<span class="math">y'=\displaystyle\frac{(cosxy)*(xy' + y)}{2y}[/spoiler]

I dunno how to get rid of the y' in the answer, that can't be right..


>>1958424
On the left you missed <span class="math">y'-y'[/spoiler] didn't you? that's what I kept running into, they cancel out, unless I'm doing it way wrong.

>>1958416
Bro there's no parenthesis, it's just "sin xy" written exactly like that.

>>1958521
"Bro", you SHOULD have used parentheses. As it's written, it's completely unclear whether you mean "the product of y and the sin of x", or "the sin of the product of x and y".

OP you in math 150?

ohhh shit, you factor out the <span class="math">\displaystyle\frac{dy}{dx}[/spoiler]

I got it now.

But, this all presumes that the equation is meant to be sin (xy)

Still no fucking idea if that's right, but hopefully this effort will count.

Thanks a ton bro/broette, you've saved my ass.

>>1958521
I missed y' - y'? What the heck are you talking about? I grouped all y' terms on the left side and factored.

If I had:

2bx - 3ax = c

You would factor out x to get:

(2b - 3a)x = c

Then divide by (2b-3a) to get

x = c/(2b-3a)

This is stuff you should know FAR before calculus...

>>1958541
no I think it's 165, Calc 1

>>1958535
I didn't write the problem. I agree that the instructor should have specified, but I'm writing what I see. The fact that this isn't clear to you is shameful, Bro.

>>1958535
the sin of the product of x and y, eh?

>>1958548
Yeah I know, it's basic algebra, hence the realization once I noticed the stupid mistake. I tend to overlook things like that when I'm worn out. Sorry!

>>1958556
Yep, when that dastardly i tempted X into giving Y the apple pi of the knowledge of true and false.