Basic partial derivative:

D[ x^2*y^4 + Sin[x*y]*z, z ]

A second derivative, in this case with respect to z and then y

D[ x^2*y^4 + Sin[x*y]*z, z, y ]

A vector of the derivatives with respect to x, y, and z.

D[ x^2*y^4 + Sin[x*y]*z, {{x,y,z}} ]