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Unformatted text preview: tangent lines. Derivatives of Exponential Functions Consider d dx f ( x ) where f ( x ) = a x : f ( x ) = lim h ! Since f (0) = lim h ! then f ( x ) = What does this say about the rate of change of any exponential? If a = 2, f (0) = lim h ! If a = 3, f (0) = lim h ! De±nition: e is the number such that lim h ! e h ± 1 h = d dx ( e x ) = 6? ± ex. At what point is the tangent line to f ( x ) = e x parallel to y = 4 x + 1? Find f ( x ) for the following functions: ex. f ( x ) = p x + 3 p x 4 p x ex. g ( x ) = ex 2 + 2 e x + xe 2 + x e 2 ex. h ( x ) = x ln 3 ± ± ln 3 ± e e...
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 Spring '08
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