Differential of a 2-form: How to Compute df Using the Wedge Product?

[tazzzdo]

Homework Statement

Compute the differentials of the following form:

Homework Equations

f = e^xy dy ^ dz

The Attempt at a Solution

I'm a little confused on how to work with the wedge product. If I'm looking for df, should I start by calculating the dual f*? Or does the dual not come into play?

 

[HallsofIvy]

No, there is no reason to worry about the dual. For any f, $df= (\partial f/\partial x)dx+ (\partial f/\partial y)dy+ (\partial f/\partial z)dz$.

If
$f= e^{xy} dy^dz$ then
$$df= (\partial e^{xy}/\partial x)dx\^dy\^dz+ (\partial e^{xy}/\partial y)dy\^dy\^dz+ (\partial e^{xy}/\partial z)dz\^dy\^dz$$
Remember, of course, that the wedge product is "anti-symmetric".

 

[tazzzdo]

So

df = ye^xy dx ^ dy ^ dz + xe^xy dy ^ dy ^ dz ? Is that the answer?