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.
Calculus through Data & Modeling: Differentiation Rules
Calculus through Data & Modeling: Differentiation Rules
This course is part of Differential Calculus through Data and Modeling Specialization
Instructor: Joseph W. Cutrone, PhD
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7 hours to complete
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This course is part of the Differential Calculus through Data and Modeling Specialization
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There are 7 modules in this course
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.
What's included
3 videos1 reading1 assignment
The formulas of this section enable us to differentiate new functions formed from old functions by multiplication or division.
What's included
2 videos1 reading1 assignment
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.
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2 videos1 reading1 assignment
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.
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1 video1 reading1 assignment
In this module, the notion of the derivative is applied to multivariable functions through the notion of partial derivatives. Algebraic rules are developed to find partial derivatives of multivariable functions as well as their geometric interpretations. The development of the tools of calculus to multivariable functions allows for further analysis of more complicated data sets.
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1 video2 readings1 assignment
In this module, we continue the application of partial derivatives to find rates of changes in any direction by developing the theory of directional derivatives and gradient vectors. These new tools of multivariable calculus can then be applied to problems in economics, physics, biology, and data science.
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1 video2 readings1 assignment
Apply the theory of this course to model a flight path for a landing aircraft.
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1 peer review
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Johns Hopkins University
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Johns Hopkins University
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