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# L12 - If a = 2 f(0 = lim h → If a = 3 f(0 = lim h → 8...

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L12 – Derivatives of Polynomials and Exponentials d dx c = c constant d dx x n = n any real 1

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d dx π 2 d dx x 52 d dx 1 x 4 2
d dx 4 x x d dx x 5 x 2 3

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Find the equation of the tangent line to f ( x ) = 3 x at x = - 1. 4
d dx cf ( x ) = c constant and f differentiable d dx [ f ( x ) ± g ( x ) ] f and g both differentiable This can be extended to Find f 0 ( x ) if f ( x ) = 6 x 3 - 3 x 2 - 12 x . 5

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Where does f ( x ) have horizontal tangent lines? d dx e x = 6
Consider d dx f ( x ) where f ( x ) = a x . f 0 ( x ) = lim h 0 Since f 0 (0) = lim h 0 then f 0 ( x ) = 7

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What does this say about the rate of change of any exponential?

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Unformatted text preview: If a = 2, f (0) = lim h → If a = 3, f (0) = lim h → 8 Def – e is the number such that lim h → e h-1 h = d dx e x = 9 At what point is the tangent line to f ( x ) = e x parallel to y = 4 x ? 10 Find f ( x ) if f ( x ) = √ x + 3 √ x 4 √ x g ( x ) = ex 2 + 2 e x + xe 2 + x e 2 h ( x ) = x ln 3-π ln 3-e e 11...
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L12 - If a = 2 f(0 = lim h → If a = 3 f(0 = lim h → 8...

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