Given the function:
$\ f(x,y,z) = x^2 + y^2 + \arctan(z) $
How can we determine if the differential $[ \mathrm{d}f(1,2,3) ]$ exists and then calculate it?
Finding all the partial derivatives and confirming that they are continuous is enough? (because we have a theorem that says "if the partial derivatives of $f$ at $(x_0, y_0, z_0)$ are continuous then there is the differential of $f$ at the specific point".