Implicit Differentiation Question - Stuck

[playdohh]

Homework Statement

Use implicit differentiation to find y' given y/(x-y) = x^2+1.

Homework Equations

The Attempt at a Solution

Hi, I'm doing an online course for Calculus 12, and I have been struggling with Implicit Differentiation. I am hoping someone could maybe help me. Thanks.

I'm not positive I'm doing this right, but maybe someone can point me in the right direction. This is what I have so far

y/(x-y) = x^2+1

y=(x^2+1)(x-y)

y' = (2x)(x-y)+(x^2+1)(1-y')

y' = 2x^2-2xy+x^2-x^2y'+1-y'

This is where I get stuck and am not sure if I'm making a mistake or know what to do next. Any help would be appreciated, thank you.

 

[playdohh]

y/(x-y) = x^2+1

y=(x^2+1)(x-y)

y' = (2x)(x-y)+(x^2+1)(1-y')

y' = 2x^2-2xy+x^2-x^2y'+1-y'

2y'+x^2y' = 3x^2-2xy+1

y'(2+x^2) = 3x^2-2xy+1

y' = (3x^2-2xy+1)/(2+x^2)

That's what I got as my continued attempt, does that look right?

 

[vela]

y/(x-y) = x^2+1

y=(x^2+1)(x-y)

y' = (2x)(x-y)+(x^2+1)(1-y')

Up to here is correct. If you did the subsequent algebra correctly, you should have the right answer.

y' = 2x^2-2xy+x^2-x^2y'+1-y'

2y'+x^2y' = 3x^2-2xy+1

y'(2+x^2) = 3x^2-2xy+1

y' = (3x^2-2xy+1)/(2+x^2)

That's what I got as my continued attempt, does that look right?

In this problem, you can solve the original equation for y. Try that and then differentiate the resulting expression. See if you get the same result.