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Unformatted text preview: h e h1 h = 1. 1 2 DERIVATIVES OF POLYNOMIALS AND EXPONENTIAL FUNCTIONS From the denition, we can get the following dierentiation formula. Theorem 1. d dx ( e x ) = e x Example 3. If f ( x ) = e xx 2 + 3 x , nd f and f 00 . Solution f ( x ) = d dx ( e xx 2 + 3 x ) = d dx ( e x )d dx ( x 2 ) + 3 d dx ( x ) = e x2 x + 3 f ( x ) = d dx ( e x2 x + 3) = d dx ( e x )2 d dx ( x ) + d dx (3) = e x2 Example 4. Find an equation of the normal line to the curve y = e xx 2 + 3 x at the point P (0 , 1). Solution Since the slope of the tangent line at the point P is y (0) = 4, we can see that the slope of the normal line is1 4 . Thus, the equation of the normal line is y1 =1 4 ( x0) , or y =1 4 x + 1 ....
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 Fall '09
 BenedictGross
 Exponential Function, Polynomials, Derivative, Exponential Functions

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