Implicit Differentiation. x^3 +y^3 =24xy.

Question

anonymous · Answer

I ended up with, but its not correct. Not sure what i did wrong.

$$y'= \frac{ -3x+24y }{ 3y-24x} $$

anonymous · Answer

Woops i ignored the squares....

anonymous · Answer

jhannybean · Answer

$$\large x^3 +y^3 = 24xy$$$$\large \frac{dx}{dy} = 3x^2 + 3y^2 y' = 24(y +xy')$$

bahrom7893 · Answer

3x^2+3y^2(dy/dx)=24(x dy/dx + y)

jhannybean · Answer

xD

anonymous · Answer

I caught my own mistake on this one.

bahrom7893 · Answer

aw too slow on my phone

jhannybean · Answer

Mwuahahaha

anonymous · Answer

I'm to tired for this, been doing calc all day lol. Sorry. Thanks for the race responses though : )

jhannybean · Answer

$$\large \frac{dx}{dy} = 3x^2 + 3y^2 y' = 24(y +xy')$$$$\large 3x^2 y' -24xy' = 24y -3x^2 $$$$\large y' = \frac{24y - 3x^2}{3x^2 -24y}$$

anonymous · Answer

Then divide out 3 from everything to simplify. I got it!!

jhannybean · Answer

$$\large y' = \frac{24y - 3x^2}{3x^2 -24y}$$$$\large y'=\frac{8y -x^2}{x^2 -8y}$$

anonymous · Answer

Yup yup!