Differentiating $w^2=h(t)$ in $\mathbb C(t)[W]/(W^2-h)$: $2w\,dw=h'(t)\,dt$ · Prove2Me

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Differentiating $w^2=h(t)$ in $\mathbb C(t)[W]/(W^2-h)$: $2w\,dw=h'(t)\,dt$ · Prove2Me