Question

implicitly differentiate. Solve for dy/dx
x^2(x-y)^2=x+y

Answer 1

Do I need to apply both the product rule and chain rule to the left side?

Answer 2

expand
x^2(x^2 -2xy+y^2) = x + y
x^4 - 2x^3y +x^2y^2 = x + y
4x^3 - (2x^3 dy/dx + 6x^2 y ) + (

yes - what i've started to do

Answer 3

can you continue

Answer 4

i am unsure as to why the x^2 changed to x^4

Answer 5

i expanded the brackets: - x^2 * x^2 = x^4
i find it easier to do these by expanding first - ita a personal thing

Answer 6

x^2y^2 - use product/ chain rule for this

Answer 7

got ya. I didn't see it at first I can go from there. I think your approach is easier than the one I was taught.

Answer 8

yea - i think so - why go for the hard way?

Answer 9

I think some professors like to do it the hard way to make them look smarter. Thanks again.

Answer 10

yw