(1)
z=e^(xy). cos(x+y)
dz = [-sin(x+y) .(dx +dy ) + cos(x+y). (xdy+ydx) ] .e^(xy)
(2)
let
u=√x
2udu = dx
∫dx/(1+3√x)
=∫ [2u/(1+3u)] du
=∫ [ (2/3) (1+3u) - 2/3]/(1+3u) du
=∫ { 2/3 - (2/3) [1/(1+3u)] } du
=(2/3)u - (2/9)ln|1+3u| + C
=(2/3)√x - (2/9)ln|1+3√x| + C
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