Using implicit differentiation: Is this correct?

[dylanhouse]

Homework Statement

I need to use implicit differentiation to find the derivative of y=sin(x+y).

Homework Equations

The Attempt at a Solution

This is what I did:

y=sin(x+y)
y'=(sin(x+y))'
y'=(1+y')(cos(x+y)) (by the chain rule)

Now, what do I do? Is this correct:

y'=cos(x+y)+cos(x+y)y'
y'-cos(x+y)y'=cos(x+y)
y'(1-cos(x+y))=cos(x+y)
y'= cos(x+y) / 1-cos(x+y)

?

 

[SammyS]

Homework Statement

I need to use implicit differentiation to find the derivative of y=sin(x+y).

Homework Equations

The Attempt at a Solution

This is what I did:

y=sin(x+y)
y'=(sin(x+y))'
y'=(1+y')(cos(x+y)) (by the chain rule)

Now, what do I do? Is this correct:

y'=cos(x+y)+cos(x+y)y'
y'-cos(x+y)y'=cos(x+y)
y'(1-cos(x+y))=cos(x+y)
y'= cos(x+y) / (1-cos(x+y) )

?

It's correct with the added parentheses.