1. ## Implicit Differentiation

I'm having trouble with this question.

Find dy/dx by implicit differentiation.

(x+y)/(x-y) = 3x

First I use the quotient rule getting:

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

Then I factor out y' and solve the equation for y' which gives me:

y' = [3x^2 - 6xy +3y^2]/[2x - 2y]

[6x - 3y - 1]/[3x + 1]

not sure what i'm doing wrong so any help would be appreciated. thanks

2. Don't use the quotient rule.

Rewrite the equation as

$\displaystyle x+y = 3x(x-y)$

$\displaystyle x + y = 3x^2 - 3xy$

and then use implicit differentiation.

3. Originally Posted by icemanfan
Don't use the quotient rule.

Rewrite the equation as

$\displaystyle x+y = 3x(x-y)$

$\displaystyle x + y = 3x^2 - 3xy$

and then use implicit differentiation.

1 + y' = 6x - 3y - 3xy'

y' + 3xy' = 6x - 3y -1

y'(1 + 3x) = 6x - 3y - 1

y' = (6x-3y-1)\(3x+1)

4. oh ok thanks.
so should I always rewrite such equations first before using implicit differentiation?

5. Originally Posted by abstraktz
oh ok thanks.
so should I always rewrite such equations first before using implicit differentiation?
no, you don't have to

but as icemanfan suggests

rewriting is just a modification to make the next steps more simple.

not all implicit differentiation would need rewriting.