The gradient of $\eta$: $\nabla\eta(x,s)=((s+rg(x))\nabla g(x),\ g(x))$ where $s+rg(x)\ge 0$ and $(0,-s/r)$ where $s+rg(x)\le 0$

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The gradient of $\eta$: $\nabla\eta(x,s)=((s+rg(x))\nabla g(x),\ g(x))$ where $s+rg(x)\ge 0$ and $(0,-s/r)$ where $s+rg(x)\le 0$ · Prove2Me