There may be a "British English", "American English" confusion here. In America we speak of things like df/dx as the "derivative", not gradient. The gradient of a function of two variables is specifically the vector
which is exactly what downthesun01 has.
We would then talk about the "derivative" in a particular direction, say at angle [itex]\theta[/itex] to the positive x-axis, as
, which is the same as the dot product of
with a unit vector in that direction, which is what mr. fantastic appears to be calling the "gradient".