Question

find the total differential of the function \\(f(x,y)=ye^{x+y}\\)

Answer 1

$f(x,y)=ye^{(x+y)}$

Total differential of the function is $d f =(\frac{\partial f}{\partial x})dx+(\frac{\partial f}{\partial y})dy$

$d f=\frac{\partial }{\partial x}(ye^{(x+y)})dx+\frac{\partial }{\partial y}(ye^{(x+y)})dy$

$d f=ye^{(x+y)}dx$ $+(ye^{(x+y)}+e^{(x+y)})dy$