# What is the derivative of y=sin(x+y)?

1. Oct 12, 2005

### mattsoto

what is the derivative of y=sin(x+y)???

what is the derivative of y=sin(x+y)???

2. Oct 12, 2005

### iNCREDiBLE

The partial derivatives of $f(x,y) = sin(x+y)$ are $\frac{df}{dx} = cos(x+y)$ and $\frac{df}{dy} = cos(x+y)$

3. Oct 12, 2005

### Diane_

mattsoto - What do you want the derivative with respect to? If it's anything other than x or y, we need to talk a bit more.

4. Oct 12, 2005

### mattsoto

the derivative is respect to y, Diane...

5. Oct 12, 2005

### HallsofIvy

Staff Emeritus
The derivative of y, given y= sin(x+ y), with respect to x, using implicit differentiation: y'= cos(x+y)(1+ y') so y'- y'cos(x+y)= cos(x+ y) and
y'= cos(x+y)/(1- cos(x+y)).

The derivative of x, given y= sin(x+ y), with respect to y (which is what you told you Diane you want, but I doubt since I would read what you originally wrote as 'the derivative OF y= ...), by implicit differentiation: 1= cos(x+y)(x'+ y) so
1- ycos(x+y)= cos(x+y)x' and x'= (1- ycos(x+y))/cos(x+y).