anonymous
  • anonymous
What is pi(sin(y)) implicitly differentiated?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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rvc
  • rvc
meaniny u want dy/dx?
anonymous
  • anonymous
Well, the whole equation is \[2xy +\pi \sin (y)=2\pi\], but I know the rest.
anonymous
  • anonymous
But, yeah. I've gotta find dy/dx.

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zepdrix
  • zepdrix
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.
zepdrix
  • zepdrix
Do you understand how to differentiate the first term? That one is kind of tricky, requires product rule.
anonymous
  • anonymous
2y(dy/dx)? Thanks! I wasn't sure if it the dy/dx was inside the parenthesis with y.
zepdrix
  • zepdrix
\[\large\rm \frac{d}{dx}2xy\quad=(2x)'y+2x(y)'\]Product rule! :) Leading to this,\[\large\rm \frac{d}{dx}2xy\quad=2y+2x\frac{dy}{dx}\]
anonymous
  • anonymous
Ohhhh! D'oh. Thank you!
zepdrix
  • zepdrix
Got the right side figured out? :) Hopefully you didn't differentiate and get 2
anonymous
  • anonymous
No, I got zero.
zepdrix
  • zepdrix
Cool

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