Answer
$4xy^3dx+6x^2y^2dy$
Work Step by Step
To find the total differential of z, denoted $dz$, use the following formula.
$dz=\frac{dz}{dx}dx+\frac{dz}{dy} dy$
which can also be written as
$dz=f_{x}(x,y)dx+f_{y}(x,y)dy$
Note that these are partial derivatives of $f(x,y)$ in terms of x and y.
$f(x,y)=z=2x^2y^3$
$dz=4xy^3dx+6x^2y^2dy$
