anonymous
  • anonymous
Help is very appreciated! Y is a differentiable function of x. Choose the alternative that is the derivative dy/dx. x^3-y^3=1 x+cos(x+y)=0 3x^2-2xy+5y^2=1 I'm doing these for homework on my AP Calc preparation course and am really confused. The teacher kind of rushed over this and I don't really understand what they meant. Thank You!
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Loser66
  • Loser66
Do you know partial derivative? implicit derivative?

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anonymous
  • anonymous
sort of, we just started
Loser66
  • Loser66
the first one x^3 +y^3 = 1 if we solve y w.r.t.x, it is hard to take derivative. Hence, we apply implicit one derivative both sides 3x^2 + 3y^2y' =0 that gives us y'= -x^2/y right?
Loser66
  • Loser66
that is it.
anonymous
  • anonymous
oh, cool
anonymous
  • anonymous
would it be positive?
anonymous
  • anonymous
oh wait, nvm
Loser66
  • Loser66
for the second one x +cos (x+y) =0 same 1-sin(x+y) *(x+y)' =0 1+ sin(x+y)(1+y') =0 so, just solve for y' that is it. do the same with the rest/
Loser66
  • Loser66
oh, I mess up at the second line, it is 1- sin...
anonymous
  • anonymous
Oh, gotcha. Is it okay if you help me with another question? If x=e^theta cos theta and y=e^theta sin theta, then, when theta=pi/2, dy/dx is...

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