# Partial and total differentiation

1. Apr 5, 2014

### Jhenrique

You can give me a good examples where $\frac{\partial}{\partial x}$ is different to $\frac{d}{dx}$ ?

Last edited: Apr 5, 2014
2. Apr 5, 2014

### Staff: Mentor

Comparing these two operators is like comparing apples and oranges.

$\frac{d}{dx}$ operates on a function of a single variable; e.g., f(x).
$\frac{\partial}{\partial x}$ operates on a function of two or more variables; e.g., g(x, y).

If you are given a function of two or more variables, such as f(x, y), but each variable is a function of one variable alone; i.e., f(x(t), y(t)), then it makes sense to talk about the total derivative df/dt.

3. Apr 8, 2014

### Jhenrique

But, I never see a total differential wrt x of a scalar or vector function f(x) be different of the partial differential wrt x of same scalar or vector function f(x).