Let g: R R be given by g(x, y, z) = (x - y sin(z), e...

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Let g: R R be given by g(x, y, z) = (x - y sin(z), e (y - x)) and let f: R R be given by f(u, v) = (u - v, uv). (a) Briefly argue that g and f are differentiable everywhere (i.e., at any x R), and use this to argue that h = fog (i.e., the function given by h(x, y, z) f(g(x, y, z))) is differentiable everywhere. = (b) Use the chain rule to compute Dh(1,2,3). (Leave numbers in the form sin(3) or e instead of approximating these numbers.) Let g: R R be given by g(x, y, z) = (x - y sin(z), e (y - x)) and let f: R R be given by f(u, v) = (u - v, uv). (a) Briefly argue that g and f are differentiable everywhere (i.e., at any x R), and use this to argue that h = fog (i.e., the function given by h(x, y, z) f(g(x, y, z))) is differentiable everywhere. = (b) Use the chain rule to compute Dh(1,2,3). (Leave numbers in the form sin(3) or e instead of approximating these numbers.)