CHAPTER Continuity CHAPTER Derivatives of Polynomials and Exponential Functions

CHAPTER Continuity Derivative of a Constant Function (d/dx) (c) = 0 (d /dx) (x) = 1 The Power Rule If n is a positive integer, then (d /dx) (x n ) = n x n-1

CHAPTER Continuity Example Find the derivatives of the given functions. a)f(x) = 3x b)g(x) = x 3 + 2x + 9

CHAPTER Continuity The Power Rule (General Rule) If n is any real number, then (x n )’ = n x n-1 The Constant Multiple Rule If c is a constant and f is a differentiable function, then [ c f(x) ]’= c f’(x)

CHAPTER Continuity Example Find the derivatives of the given functions. a) f(x)= -3x 4 b)f(x) =  x. ___

CHAPTER Continuity The Sum Rule If f and g are both differentiable, then [ f(x) + g(x)]’ = f’(x) + g’(x) The Difference Rule If f and g are both differentiable, then [ f(x) - g(x)]’ = f’(x) – g’(x)

CHAPTER Continuity Example Find the derivatives of the given functions. a) y = (x 2 – 3) / x b) f(x) = x 2 _ 7x + 55.

CHAPTER Continuity Definition of the Number e e is the number such that lim h  0 (e h – 1) / h = 1. Derivative of the Natural Exponential Function ( e x )’ = e x.

CHAPTER Continuity Example Differentiate the functions: a) y = x e x b) y = e x