# Partial differential = the change?

1. Nov 21, 2012

partial differential = the change??

1. The problem statement, all variables and given/known data

How is
Δy/Δx = $\partial y$ / $\partial x$ ?

I just don't know the logic behind this.

2. Nov 22, 2012

### lurflurf

Re: partial differential = the change??

That is only approximately or asymptotically true. If Δy and Δx are small Δy/Δx will be near ∂y / ∂x.

3. Nov 22, 2012

### SammyS

Staff Emeritus
Re: partial differential = the change??

Do you understand how $\Delta y/\Delta yx\approx dy/dx\ ?$

Usually, x & y are independent variables -- and often there are additional independent variables.

If f is a function of independent variables, x and y, then we write f(x,y).

$\partial f/\partial x\ \$ is essentially $\ \ df/dx\ \$ if we treat y as being held at some fixed value.

Then $\ \ \Delta f/\Delta x \approx \partial f/\partial x\ \$ keeping y fixed at some value.

By the Way: If x & y are independent variables, then $\ \ \partial y/\partial x=0 \ .$