How to differentiate e^(x+y) for x?

[gtfitzpatrick]

Homework Statement

if f(x,y) is e^(x+y) am i right in saying dy/dx is e^(x+y)

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

If y is not a function of x, dy/dx makes no sense at all! (Except for dy/dx= 0.)
The notation f(x,y)= e^x+y implies that x and y are independent variables. Without further information, you can find $\partial f/\partial x$ or $\partial f/\partial y$ but not dy/dx.

If, for example, you know that f(x,y)= e^x+y= constant, then you can use "implicit differentiation": (1+ dy/dx)e^x+y= 0 and determine that dy/dx= -1.