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**Unformatted text preview: **Section 3.1: Derivatives of Polynomials and Exponential Functions Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) Power Rule If f ( x ) = x n ( n is any real number) then f ( x ) = nx n- 1 . Example : f ( x ) = x 1000 f ( x ) = f ( t ) = t 3 f ( t ) = f ( x ) = x f ( x ) = f ( x ) = c (where c is a constant) f ( x ) = f ( r ) =- 1 r 2 f ( r ) = f ( x ) = x f ( x ) = f ( x ) = 3 x 2 f ( x ) = f ( x ) = x x f ( x ) = Remark : f = df dx (Leibniz notation) Compute Derivatives of New Functions New functions are formed from old functions by addition, subtraction, multiplication or division. If we know the derivatives of old functions, we can compute the derivatives of the new functions based on the following rules: Assume that the derivatives of f, g exist (i.e., f, g are differentiable), then The constant multiple rule : d dx [ cf ] = c df dx ( cf ) = cf ( c is a constant) The sum or difference rule...

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