# Thread: Find derivative of y when....

1. ## Find derivative of y when....

http://i39.tinypic.com/nnqgk8.jpg

I got something close to the second choice but not exact.
Can you show how you got it?

2. Originally Posted by janedoe
http://i39.tinypic.com/nnqgk8.jpg

I got something close to the second choice but not exact.
Can you show how you got it?
$y=\sin\!\left(x+y\right)$

By implicit differentiation [and chain rule], we have $\frac{\,dy}{\,dx}=\cos\!\left(x+y\right)\cdot\left (1+\frac{\,dy}{\,dx}\right)\implies \frac{\,dy}{\,dx}=\cos\!\left(x+y\right)+\cos\!\le ft(x+y\right)\frac{\,dy}{\,dx}$

Can you finish off the problem?