x^4 + xy - y^2 = xy^2 implicit and exmplicit differentiation

Question

I posted a question similar to this and now I understand how to do implicit differentiation but my derivative is still not turning out right.

I took
x^4 + xy − y^2 = xy^2

using what I learned on the previous question I took the derivative after moving all terms to one side to be:

4x^3+x dy/dx+ y*1 -2y dy/dx -x dy/dx +y^2.

I moved all terms without a dy/dx to one side and factored dy/dx out on the other.

I got:

dy/dx [x-2y-x2y]=-4x^3-y-y^2

Then I divided by what was multiplying dy/dx and got:

dy/dx= (-4x^3-y-y^2)/(x-2y-x2y)

I submitted this for my answer but got it wrong. Could you please tell me what I did wrong in regards to following the rules from my previous question.

Answer 1

Let us try this step by step and see what comes out:

 

x⁴ + xy - y² -  xy² = 0

 

Differentiate:

 

4x³ + (y + xy') - 2yy' - (y² + 2yy'x) = 0 

 

Collect terms with y':

 

4x³ + y + y'(x - 2y - 2xy) - y² = 0

 

Isolate y':

 

y'(x - 2y - 2xy) = -4x³ - y + y²

 

y' = (y² - y - 4x³) / (x - 2y - 2xy)

 

The difference between my answer and your answer is that I got a +y² in the numerator where you got a -y².  Check the math carefully, and see if this works.