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- TL;DR Summary
- Let f (x, y) and g(x, y) be continuously differentiable real-valued functions in a region R.

Show that ##\displaystyle\oint_C f\nabla g \cdot dr = -\displaystyle\oint_C g\nabla f \cdot dr## for any closed curve in R

I don't have any idea to answer this question. So, any math help will be accepted.

I know ##\nabla fg = f\nabla g + g\nabla f \rightarrow (1) ## But I don't understand to how to use (1) here?

I know ##\nabla fg = f\nabla g + g\nabla f \rightarrow (1) ## But I don't understand to how to use (1) here?

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