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 .

• Toán học
• Mathematics 53
• Lecture Mathematics 53
• Derivatives of logarithmic
• Exponential functions
• Logarithmic functions
• Logarithmic differentiation
• Integrals yielding logarithmic
• Integrals of exponential functions
• Natural logarithmic function
• Inverse circular functions
• Integrals yielding
• Derivatives of inverse circular functions
• Graphs of inverse circular functions
• Hyperbolic functions
• Inverse hyperbolic functions
• Derivatives of hyperbolic functions
• Indeterminate forms
• L’Hôpital’s rule
• Polynomial functions
• Basic types of functions
• Constant functions
• Linear functions
• Limit of a function
• One sided limits
• Limit theorems
• One sided limit
• Infinite limits
• The greatest integer function
• Vertical asymptotes
• Infinity formal definition
• Intuitive definition
• Horizontal asymptotes
• Continuity of functions
• Continuity on an interval
• Essential discontinuity
• The intermediate value theorem
• The squeeze theorem
• Trigonometric functions
• Continuity of trigonometric functions
• Differentiation rules
• The tangent line
• Definition of the derivative
• The chain rule
• Chain rule theorem
• Funtion theorem
• Geometric interpretation of differentiability
• Higher order derivatives
• Implicit differentiation
• Local linear approximation
• Rates of change
• Rectilinear motion
• Position function
• Instantaneous velocity
• Related rates
• Function of time
• Problem on related rates
• Numerical facts
• Mean value theorem
• Relative extrema
• Critical numbers
• Decreasing functions
• The second derivative test
• Points of inflection
• Graphing polynomials
• Second derivative
• Graphing functions
• Vertical asymptotes
• Oblique asymptotes
• Absolute extrema
• Bounded intervals
• One relative extremum
• Absolute maximum
• Optimization word problems
• Optimization problems
• Solving optimization problems
• Integration by substitution
• Theorems on antidifferentiation
• Substitution rule
• Particular antiderivatives
• Application to rectilinear motion
• Plane region
• The definite integral
• Properties of the definite integral
• General antiderivative
• The second fundamental theorem of calculus
• Arc length
• Area of a plane region
• Horizontal rectangles
• Volumes of solids of revolution
• Washer method
• Cylindrical shell method
• Solids of revolution