Question

Use implicit differentiation to find dy/dx
x^3+3x^2y+y^3=8

Answer 1

dy/dx=y' (easier to read, imo).

Then:
3x²+6xy+3x²y'+3y²y'=0.

Now try to isolate y' (solve for y').

Answer 2

3x^2y'+3y^2y'=-3x^2-6xy
?
then add like terms to
6x^2y'=-3x^2-6xy
then divide by 6x^2
which equals
\[\frac{ -3x^2-6xy }{ 6x^2 }\]

Answer 3

I get:

y'(3x²+3y²)=-3x²-6xy.

So \(y'=\dfrac{-3x^2-6xy}{3x^2+3y^2}=-\dfrac{3x(x+2y)}{3(x^2+y^2)}=-\dfrac{x(x+2y)}{x^2+y^2}\)

Answer 4

Thee are no like terms...

Answer 5

ok I got it thanks

Answer 6

YW!