Calculus through Data & Modeling: Differentiation Rules continues the study of differentiable calculus by developing new rules for finding derivatives without having to use the limit definition directly. These differentiation rules will enable the calculation of rates of change with relative ease the derivatives of polynomials, rational functions, algebraic functions, exponential and logarithmic functions, and trigonometric and inverse trigonometric functions. Once these rules are developed, they are then applied to solve problems involving rates of change and the approximation of functions.
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第 3 門課程（共 4 門）
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完成時間大約為8 小時
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可靈活調整截止日期
根據您的日程表重置截止日期。
可分享的證書
完成後獲得證書
100% 在線
立即開始，按照自己的計劃學習。
第 3 門課程（共 4 門）
中級
完成時間大約為8 小時
英語（English）
字幕：英語（English）
提供方
约翰霍普金斯大学
The mission of The Johns Hopkins University is to educate its students and cultivate their capacity for life-long learning, to foster independent and original research, and to bring the benefits of discovery to the world.
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完成時間為 1 小時
Derivatives of Polynomial, Exponential, and Logarithmic Functions
In previous course, we defined and calculated the derivative as a limit. In this module, we will examine the derivatives of some important functions, including polynomials, exponentials, logarithms, and trigonometric functions. We will also learn differentiation rules which will help us to compute derivatives more efficiently. Finally, we will generalize the idea of a derivative to multivariable functions, and learn how to find derivatives and rates of change on a graph in space.
完成時間為 1 小時
3 個視頻 （總計 36 分鐘）, 1 個閱讀材料, 1 個測驗
完成時間為 1 小時
The Product and Quotient Rules
The formulas of this section enable us to differentiate new functions formed from old functions by multiplication or division.
完成時間為 1 小時
2 個視頻 （總計 21 分鐘）, 1 個閱讀材料, 1 個測驗
完成時間為 1 小時
Derivatives of Trigonometric Functions
Before starting this module, please review trigonometric functions, in particular their graphs. In this module, we will develop formulas to find derivatives for the common trigonometric functions of sine and cosine. Together with the product and quotient rules, the derivatives for the remaining trigonometric functions are formulated. These new derivative formulas are then added to our catalog to use and apply to solve problems related to rates of change.
完成時間為 1 小時
2 個視頻 （總計 23 分鐘）, 1 個閱讀材料, 1 個測驗
完成時間為 1 小時
The Chain Rule
Many functions are created through composition of other functions. In this module, one of the most important of the differentiation rules of this course is developed which will allow us to find derivatives of the compositions of functions. This rule is called the chain rule and has a variety of applications.
完成時間為 1 小時
1 個視頻 （總計 15 分鐘）, 1 個閱讀材料, 1 個測驗
關於 Differential Calculus through Data and Modeling 專項課程
This specialization provides an introduction to topics in single and multivariable calculus, and focuses on using calculus to address questions in the natural and social sciences. Students will learn to use the tools of calculus to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.
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