tailieunhanh - Lecture Mathematics 53: Lecture 5.1 - UP Diliman

Lecture Mathematics 53 - Lecture provides knowledge of the derivatives of logarithmic and exponential functions. This chapter presents the following content: Exponential and logarithmic functions, derivatives of logarithmic functions, logarithmic differentiation, derivatives of exponential functions,. | . Derivatives of Logarithmic and Exponential Functions Mathematics 53 Institute of Mathematics UP Diliman Instituteof Mathematics UP Diliman Derivatives of Logarithmic and Exponential Functions Mathematics 53 1 30 For today Exponential and Logarithmic Functions Derivatives of Logarithmic Functions Logarithmic Differentiation Derivatives of Exponential Functions 5 Derivative of f x g x where f x 0 Instituteof Mathematics UP Diliman Derivatives of Logarithmic and Exponential Functions Mathematics 53 2 30 Definition Q If a 0 and a 1 then the exponential function with base a is f x ax. 4 If a 0 and a 1 the logarithmic function with base a written as f x loga x is the inverse function of the exponential function with base a. o y loga x if and only if x ay o loga ax x for all x 2 JR. o alogax x for all x 0 What are the derivatives of these functions Instituteof Mathematics UP Diliman Derivatives of Logarithmic and Exponential Functions Mathematics 53 4 .