103 Section 5.4 Exponential Functions: Differentiation and Integration Course Number Section 5.4 Exponential Functions: Differentiation and Integration Instructor In this lesson you learned about the properties of the Objective: Date natural exponential function and how to find the derivative and antiderivative of the natural exponential function. The Natural Exponential Function (Pages What you should The inverse function of the natural logarithmic function How to develop properties of the natural (x) ln is called the natural exponential = f x exponential function function and is denoted by (x) = . That is, f ex = y ex if and only if = ln . x y Solve 7 59 for Round to three decimal Example 1: = e x. places. 6.190 x Example 2: Solve 4 ln 5x 28 for Round to three decimal = x. places. 219.327 x Complete each of the following operations with exponential functions. = . ea eb ea+b = . e eb List four properties of the natural exponential function. The domain of = is and the range is (0, f(x) ex The function = is continuous, increasing, and one-to- f(x) ex one on its entire domain. The graphs of = is concave upward on its entire f(x) ex domain.
Section 5.4 Exponential Functions: Differentiation and Integration 103 Section 5.4 Exponential Functions: Differentiation and Integration Objective: In this lesson you learned about the properties of the natural exponential function and how to find the derivative and antiderivative of the natural exponential function. The Natural Exponential Function (Pages The inverse function of the natural logarithmic function f (x) = ln x is called the natural exponential Course Number Instructor Date What you should How to develop properties of the natural exponential function function and is denoted by f (x) = ex . That is, y = ex if and only if x = ln y . Example 1: Solve e 7 = 59 for x. Round to three decimal places. x 6.190 Example 2: Solve 4 ln 5x = 28 for x. Round to three decimal places. x 219.327 Complete each of the following operations with exponential functions. ea eb = ea+b . e = . eb List four properties of the natural exponential function. The domain of f(x) = ex is and the range is (0, The function f(x) = ex is continuous, increasing, and one-to- one on its entire domain. The graphs of f(x) = ex is concave upward on its entire domain.