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 modules

Gain insight into a topic and learn the fundamentals.

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Intermediate level

Some related experience required

8 hours to complete

Flexible schedule

Learn at your own pace

7 modules

Gain insight into a topic and learn the fundamentals.

117 reviews

Intermediate level

Some related experience required

8 hours to complete

Flexible schedule

Learn at your own pace

Skills you'll gain

Details to know

Shareable certificate

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Assessments

6 assignments¹

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Taught in English

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There are 7 modules in this course

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.

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

3 videos Total 36 minutes

Introduction to Differentiation Rules 1 minute
Derivatives of Polynomial Functions 16 minutes
Derivatives of Exponential Functions 18 minutes

1 reading Total 10 minutes

Notes: Derivatives of Polynomial, Exponential, and Logarithmic Functions 10 minutes

1 assignment Total 30 minutes

Derivatives of Polynomial, Exponential, and Logarithmic Functions 30 minutes

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.

What's included

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.

What's included

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.

What's included

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.