# Partial Derivative

1. Jan 19, 2012

### MHD93

let f(x, y') = x + y'
where y' = dy/dx
then is it true, and why, that the partial derivative of f with respect to y' = 1
in this case we consder dx/dy' = 0, as if they are independent of each other.

2. Jan 19, 2012

### obafgkmrns

3. Jan 19, 2012

### MHD93

but since y' = dy/dx , then y depends on x, and y' might depend on x too
therefore there might be a relation between x and y', and dx/dy' doesn't necessarily equal zero

4. Jan 19, 2012

### obafgkmrns

To tell the truth, that bothered me as well when I first encountered the concept. The professor was confused as to why I even asked the question. Consider a function f(x,y). Is there any problem with defining partial derivatives with respect to x and y? What if, unbeknownst to you, y is actually a function of x? Well, the answer is no problem. As far as f(x,y) is concerned, y is just a parameter that can take any value. You can substitute the relationship y(x) into the mix after you take the partial derivative.