## anonymous one year ago 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!

1. 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.

2. 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

3. Zale101

Clear? @brando86

4. anonymous

Ah, yes I understand it now. Thanks!

5. Zale101

No problem! Tag me when you get stuck at something.