Question

What is pi(sin(y)) implicitly differentiated?

Answer 1

meaniny u want dy/dx?

Answer 2

Well, the whole equation is \[2xy +\pi \sin (y)=2\pi\], but I know the rest.

Answer 3

But, yeah. I've gotta find dy/dx.

Answer 4

Differentiating the term you indicated gives:\[\large\rm \frac{d}{dx}\pi \sin (y)\quad=\pi \cos(y)\frac{d}{dx}y\]By the chain rule^\[\large\rm \frac{d}{dx}\pi \sin (y)\quad=\pi \cos(y)\frac{dy}{dx}\]

pi is just a constant, treat it as such.
Don't attempt to apply product rule or anything fancy when you see the pi.

Answer 5

Do you understand how to differentiate the first term?
That one is kind of tricky, requires product rule.

Answer 6

2y(dy/dx)?
Thanks! I wasn't sure if it the dy/dx was inside the parenthesis with y.

Answer 7

\[\large\rm \frac{d}{dx}2xy\quad=(2x)'y+2x(y)'\]Product rule! :)
Leading to this,\[\large\rm \frac{d}{dx}2xy\quad=2y+2x\frac{dy}{dx}\]

Answer 8

Ohhhh! D'oh. Thank you!

Answer 9

Got the right side figured out? :)
Hopefully you didn't differentiate and get 2

Answer 10

No, I got zero.

Answer 11

Cool