anonymous
  • anonymous
Using implicit differentiation, find the derivative y = -ln(4x^2 + 8y^2) What I got so far: y' = -(8x+16yy')/(4x^2 + 8y^2) How would I solve for y' algebraically? Thanks!
Mathematics
katieb
  • katieb
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Zale101
  • Zale101
\(y = -ln(4x^2 + 8y^2)\) \(y'=\large -\frac{1}{4x^2+8y^2}*8x+16y*y'\) \(y'=\LARGE -\frac{8x+16y*y'}{4x^2+8y^2}\) Factor out the y' by multiplying both sides by 4x^2+8y^2, then expand it.
Zale101
  • Zale101
\(\Large y'=\frac{16y*y'-8x}{4x^2+8y^2}\) \( (4x^2+8y^2)y'=\Large{\frac{16y*y'-8x}{4x^2+8y^2}}*(4x^2+8y^2)\) \( (4x^2+8y^2)y'=16y*y'-8x\) distribute the y' in then do some further simplifying and canceling
Zale101
  • Zale101
Clear? @brando86

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anonymous
  • anonymous
Ah, yes I understand it now. Thanks!
Zale101
  • Zale101
No problem! Tag me when you get stuck at something.

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