Question

u( x, y) = e^x(xsiny+ycosy) find the differentials

Answer 1

$du\left( x,y \right) =u'_xdx+u'_ydy=\\=\left( e^x\sin y+xe^x\sin y+e^xy\cos y \right) dx+\left( e^xx\cos y+e^x\cos y-e^xy\sin y \right) dy$