Johns Hopkins University
Calculus through Data & Modeling: Differentiation Rules
Johns Hopkins University

Calculus through Data & Modeling: Differentiation Rules

This course is part of Differential Calculus through Data and Modeling Specialization

Taught in English

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Joseph W. Cutrone, PhD

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Course

Gain insight into a topic and learn the fundamentals

4.8

(47 reviews)

Intermediate level
Some related experience required
7 hours (approximately)
Flexible schedule
Learn at your own pace

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Assessments

6 quizzes

Course

Gain insight into a topic and learn the fundamentals

4.8

(47 reviews)

Intermediate level
Some related experience required
7 hours (approximately)
Flexible schedule
Learn at your own pace

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This course is part of the Differential Calculus through Data and Modeling Specialization
When you enroll in this course, you'll also be enrolled in this 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 quiz

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 quiz

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.

What's included

2 videos1 reading1 quiz

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.

What's included

1 video1 reading1 quiz

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.

What's included

1 video2 readings1 quiz

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.

What's included

1 video2 readings1 quiz

Apply the theory of this course to model a flight path for a landing aircraft.

What's included

1 peer review

Instructor

Instructor ratings
4.8 (11 ratings)
Joseph W. Cutrone, PhD

Top Instructor

Johns Hopkins University
19 Courses394,111 learners

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