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.
This course is part of the Differential Calculus through Data and Modeling Specialization
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Differential Calculus through Data and Modeling SpecializationJohns Hopkins UniversityAbout this Course
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Course 3 of 4 in the
Intermediate Level
Approx. 8 hours to complete
English
Subtitles: English
Flexible deadlines
Reset deadlines in accordance to your schedule.
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Course 3 of 4 in the
Intermediate Level
Approx. 8 hours to complete
English
Subtitles: English
Offered by
Johns Hopkins University
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.
Syllabus - What you will learn from this course
1 hour to complete
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.
1 hour to complete
3 videos (Total 36 min), 1 reading, 1 quiz
1 hour to complete
The Product and Quotient Rules
The formulas of this section enable us to differentiate new functions formed from old functions by multiplication or division.
1 hour to complete
2 videos (Total 21 min), 1 reading, 1 quiz
1 hour to complete
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.
1 hour to complete
2 videos (Total 23 min), 1 reading, 1 quiz
1 hour to complete
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.
1 hour to complete
1 video (Total 15 min), 1 reading, 1 quiz
About the Differential Calculus through Data and Modeling Specialization
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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