Implicit Differentiation question...I'll post what I keep getting

Question

anonymous · Answer

So my question is
$$x^2 + xy - y^3 = xy^2$$

anonymous · Answer

so after taking the derivative of both sides I get

$$2x + (y + x \frac{ dy }{ dx }) - 3y^2 * \frac{ dy }{ dx } = 2xy * (y + x \frac{ dy }{ dx })$$

look right so far?

zzr0ck3r · Answer

yes

jkristia · Answer

I get the same - yes

zzr0ck3r · Answer

xy^2 would be y^2 + x 2y(dy/dt) no?

jkristia · Answer

actually - no I do not get the same on the right side, let me double check my calculation

anonymous · Answer

I'm not sure there is no parenthesis around the xy so SHOULD it be x * y²?

jkristia · Answer

I get x2yy' + y^2 on the right

jkristia · Answer

xy^2 -> x(2x y') + y^2(1)

zzr0ck3r · Answer

rhs xy^2 = d(x)/dx*y^2 + d(y^2)/dx * x = 1*y^2+ 2y(dy/dx)*x

zzr0ck3r · Answer

um where you getting x^2?

jkristia · Answer

sorry x(2yy'), not x(2xy')

zzr0ck3r · Answer

word

anonymous · Answer

alright so I think my problem is...I'm counting xy² as (xy)² instead of x * y² ...alright let me do this out again...thanks guys

zzr0ck3r · Answer

right

anonymous · Answer

ahh, yes that was my problem. now I get

$$\frac{ dy }{ dx } = \frac{ y² - y - 2x }{ x - 3y² - 2xy }$$

look right?