5.2 Derivatives of General Exponentials

1 52derivativesofgeneralexponentialsnotebook

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Unformatted text preview: lim bx ­ 1 x 0 x y = bx dy = kbx dx y = ln b 2 3 4 5 6 Describe any patterns that you see in the table. 1 5.2 Derivatives of General Exponentials.notebook June 04, 2012 The Derivative of the General Exponential Function, f(x) = bx lim bh ­ 1 = ln b h 0 h lim eh ­ 1 = ln e = 1 h 0 h For the function f(x) = bx, f'(x) = (ln b) x bx For the function f(x) = ex, f'(x) = (ln e) x ex But, ln e = 1 ∴ f'(x) = ex For the function f(x) = bg(x), f'(x) = bg(x) x (ln b) x g'(x) Example #1: Differentiate each of the following functions. (a) y = 42x (b) f(x) = 54x ‐ 3 (c...
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