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所在平台: Udemy |
课程主页: https://www.udemy.com/course/calculus-1-derivatives-of-math-functions-review-course/
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课程名称：微积分1：数学函数的导数复习课程 课程概述：本课程专注于函数的导数，旨在帮助大学生和高年级中学生（如参加AP微积分AB的学生）掌握微积分第一学期中常见的导数计算。课程内容涵盖了初学者在学习导数时所需的重要概念和技巧。 主要主题： 1. 常数的导数 - 包括整数及特殊常数如e和π的例子。 2. 幂法则与常数倍法则 - 变量的幂计算。 3. 有理函数的导数。 4. 平方根与根式函数的导数。 5. 多项式函数的导数计算 - 采用和差法则。 6. 三角函数的导数 - 包括sin、cos、tan、sec、cot、csc。 7. 平均变化率与瞬时变化率的区别。 8. 切线方程的书写。 9. 导数的极限定义。 10. 导数极限定义的替代形式。 11. 指数函数的导数 - 常数的变量幂。 12. 自然对数函数的导数 - ln x。 13. 对数函数的微分。 14. 乘法法则和除法法则 - 处理乘除法。 15. 链式法则 - 包含多个实例的函数导数。 16. 隐式微分 - 处理多个变量（如x和y）的表达式的导数。 17. 反三角函数的导数。 18. 对数微分。 19. 自由响应视频测验。 通过本课程，学生将能有效掌握导数的基本概念及计算方法，为他们的微积分学习打下坚实基础。
This calculus 1 derivatives course focuses on differentiating functions. It explains how to find the derivatives of functions that you will typically encounter in your first semester calculus. This course is for university students taking college calculus and high school students who are taking AP Calculus AB.Here is a list of topics:1. Derivatives of Constants - Examples Include Integers and special constants such as e and pi2. The Power Rule and Constant Multiple Rule - Variables Raised To a Constant3. Derivatives of Rational Functions - 4. Derivatives of Square Root and Radical Functions5. How to Differentiate Polynomial Functions Using The Sum and Difference Rule6. Derivatives of Trigonometric Functions - sin, cos, tan, sec, cot, csc7. Average Rate of Change vs Instantaneous Rate of Change8. Writing Equations of the Tangent Line9. Limit Definition of the Derivative Process10. Alternative Form of Limit Definition of Derivative 11. Derivatives of Exponential Functions - Constants Raised To a Variable12. Derivatives of Natural Log Functions - Ln x13. Differentiation of Logarithmic Functions14. The Product rule and Quotient Rule - Multiplication and Division15. The Chain Rule - Plenty of Examples - Differentiating functions within functions16. Implicit Differentiation - Derivatives of Expressions With Multiple Variables such as x and y17. Derivatives of Inverse Trigonometric Functions18. Logarithmic Differentiation19. Free Response Video Quiz
