Question

Find a function f such that

Answer 1

\[\textbf{F} = \nabla f \]
\[\textbf{F} (x,y) = (1+ex)e^{xy}i+x^2e^{xy}j\]

Answer 2

It's just towards the end I'm not exactly sure what to do, like I have it all done, so I integrated (1+xy)e^(xy) and found the partial of y which gave me \[x^2e^{xy}+g'(y)\]

Answer 3

\[f_x = (1+xy)e^{xy}~~~~~~f_y=x^2e^{xy}\]

\[\int\limits (1+xy)e^{xy}dx \implies\] oh I think I was suppose to integrate respect to dy?

Answer 4

im here

Answer 5

so we've come to gradient functions now have we

Answer 6

Oh wait nvm, so integrated all of that and got \[\frac{ e^{xy} }{ y }+\frac{ e^{xy} }{ y }(xy-1)+g(y)\]