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Let $f: \mathbb{R}^3 \to \mathbb{R}$ and $g: \mathbb{R} \to \mathbb{R}$ be differentiable. Let $F: \mathbb{R}^2 \to \mathbb{R}$ be defined by the equation $$F(x,y)=f(x,y,g(x,y)).$$ (a)Find $DF$ in terms of the partials of $f$ and $g$.

(b) If $F(x,y)=0$ for all $(x,y)$, find $D_1g$ and $D_2g$ in terms of the partials of $f$.

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    Ah, you mean $g:\Bbb R^2\to\Bbb R$..2012-10-12

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