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That fgis di erentiable at every point x2Uand that its derivative is equal to f(x)g0(x)g(x)f0(x) = fDg gDf Note that this derivative is unique by Theorem 912 in Rudin 3 Let T be a linear transformation from Rn to R m Show that T Rn!R is di erentiable as a mapIndian Restaurant SHANTI q X C f B A X g V e B q X C h V eGiven g(x) = 4 – x, evaluate at x = t To evaluate this function at x = t, I'll need to plug t into every instance of x in the formula for the function g g(3) = 4 – (t) = 4 – t There's nothing more I can do with this, and I can't find a fully numerical value because I don't have a number to plug in for the t So my answer is Chapter 6 Notes "¯Œ^ ƒ~ƒfƒBƒAƒ€ ƒXƒgƒŒ[ƒg •"¯

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