Answer
$dz=e^xsinydx+e^xcosydy$
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.
$z=e^xsiny$
$dz=e^xsiny dx+e^xcosy dy$
