Conservative Vector Field!!!

Hi, for the following problem, it says both the vector fields are conservative and therefore will have potential functions.

Now, we know that if F is conservative then curl F = 0, which is true for the first vector field and the potential function for the first one is:

6x^2y+6y^2z

but it looks like the second vector field is not conservative. Please help me out with the second vector field...I dont know if it has a potential function.... (Speechless)

many Thanks,

For each of the conservative vector fields below, find a potential function f.

1. https://instruct.math.lsa.umich.edu/...050a1ac8a1.png

2. https://instruct.math.lsa.umich.edu/...73134bba41.png

Hi there

The second vectorfield is conservative, Curl is zero.

I think you might have made some mistake perhaps when calculating


So try that again.
The first one is correct.

Thanks!!

Yup, made a mistake in doing the curl...

The potential function is 8ye^(xz) + K...