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dan815

g(x,y) = e^xsin(y)
then
f(x,y) = del (g) = d/dx(g) i + d/dy(g) j
it does work out

In R² vector field F  is conservative if:

δM/δy = δN/δx

Where  F = M×i  +  N×j

The solution is

δM/δy  = δN/δx     ⇒  eˣ×cosy  = eˣ×cosy         The vector field is conservative

The Potential Function is:

U =  - eˣ×cosy +eˣ×siny

The vector field         f = eˣ×siny i + eˣ×cosy j

δM/δy  = δN/δx      ⇒  eˣ×cosy  = eˣ×cosy

Then the vector field is conservative

Could be expressed as :  f = grd×U

To find the potential function:

δM/δy =  eˣ×siny        ⇒  ∫dM = ∫eˣ×siny×dy   ⇒ M = - eˣ×cosy + g(y)

δN /δx = eˣ×cosy       ⇒  g´(y) = eˣ×cosy     g(y) =  eˣ×siny

U =  - eˣ×cosy +eˣ×siny

Related Link : https://brainly.com/question/11622971

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