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Unformatted text preview: h e h-1 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 x-x 2 + 3 x , nd f and f 00 . Solution f ( x ) = d dx ( e x-x 2 + 3 x ) = d dx ( e x )-d dx ( x 2 ) + 3 d dx ( x ) = e x-2 x + 3 f ( x ) = d dx ( e x-2 x + 3) = d dx ( e x )-2 d dx ( x ) + d dx (3) = e x-2 Example 4. Find an equation of the normal line to the curve y = e x-x 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 is-1 4 . Thus, the equation of the normal line is y-1 =-1 4 ( x-0) , or y =-1 4 x + 1 ....
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