Guichard 16.3.5

TheMeansOfProduction
Fri, 26 Jan 2018 15:41:38 +0000
Questions

In Guichard 16.3.5, we are asked to ``find an $f$ so that $\nabla f=\left<y\cos x,\sin x\right>$, or explain why there is no such $f$."

We know such an $f$ exists since $$\frac{\partial}{\partial y}(y\cos x)=\cos x=\frac{\partial}{\partial x}\sin x.$$ I'll leave it to someone else to find $f$.