Word Count : 299

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We are asked to compute the derivative of (g \circ f) manually. Let’s go step by step. We are given: [ f: \mathbb{R} \to \mathbb{R}^2, \quad f(t) = (t, t^2), ] [ g: \mathbb{R}^2 \to \mathbb{R}^3, \quad g(x,y) = (x^2, xy, y^2 - x^2). ] First, compute (g \circ f(t)): [ g(f(t)) = g(t, t^2) = \big( (t)^2, (t)(t^2), _______ ____ _________ _______ ___ ___.
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