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- Let g(x) and h(y) be differentiable functions, and let f(x, y) = h(y)i+ g(x)j. Can f have a potential F(x, y)? If so, find it.

You may assume that F would be smooth.

(Hint: Consider the mixed partial derivatives of F.)

I don't have any idea about how to use the hint given by the author.

Author has given the answer to this question i-e

I don't understand how did the author compute this answer.

Would any member of Physics Forums enlighten me in this regard?

Any math help will be accepted.

Author has given the answer to this question i-e

**F(x,y) = axy + bx + cy +d.**I don't understand how did the author compute this answer.

Would any member of Physics Forums enlighten me in this regard?

Any math help will be accepted.