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**Unformatted text preview: **1 3.10 Derivatives of General Exponential and Log Functions page 192 2 Objectives 1. Find derivatives of general exponential functions, a x . 2. Find derivatives of functions involving the log function. 4. Find derivatives using log differentiation. 5. Find derivatives of the hyperbolic functions. 3 From sec 2: Exponential Functions: D x [a x ] ( 29 ( 29 ) ( ' ) ( ' , ) ( ' 1 , 1 lim 1 lim lim lim ) ( ' f a x f so f h a a h a h as h a a h a a h a a a h a a x f x h h h h x h x h x h x h x h x h = →- =- →- =- =- =- = → → → + → Which means, the derivative of an exponential is proportional to the function itself. 4 General Exponential Rule: D x [a x ] [ ] ( 29 [ ] [ ] [ ] ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( a a a dx d a a a e e dx d e dx d a dx d x x x x a x a x a x ⋅ = ∴ ⋅ = ⋅ = = = 5 ( 29 ) 1 2 )( 5 ln( 5 ) 5 ln( 5 5 #18. 197, page 2 2 2 2- =- = =--- x dx dy x x dx d dx dy y x x x x x x 6 Page 198, #26 Find the equation of the line tangent to the curve f(x) = π 3x+9 at x = 1....

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