Question

(a) find a function f such that f = ∇f and (b) use part (a) to evaluate f(x,y)=xy^2i+x^2yj

Answer 1

f = U i + V j
∇f = Ux i + Vy j

So
Ux=U ⇒ U= g1(y)*e^x
Vy=V ⇒ V= g2(x)*e^y

For part 2, evaluate what ??