Calculus through Data & Modeling: Differentiation Rules from Coursera

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Syllabus

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.

The Product and Quotient Rules

The formulas of this section enable us to differentiate new functions formed from old functions by multiplication or division.

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.

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.

Partial Derivatives

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.

Directional Derivatives and Gradient Vectors

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.

Final Project: Flight Path

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

Good to know

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Provides a solid foundation for beginners who are interested in Calculus and its applications

Taught by Joseph W. Cutrone, PhD, who is recognized for their work in Calculus

Develops skills and knowledge that are highly relevant to learners who want to pursue a career in data science

Offers a comprehensive study of Calculus through Data & Modeling

Reviews summary

Calculus 2: understanding differentiation rules

Learners say that this course is a great course that covers advanced mathematics in differentiation of single and multivariable functions, among other topics. Many of the reviews highly recommend this course, especially for those who have taken the first course in the specialization. The exercises require a lot of work, but many students find them very helpful for understanding the material. Overall, students find the instructor to be engaging and the lectures to be well explained.

Lot of exercises

"The exercises require a lot of work and understanding how-to-do it."

"Really nice course. Everything was clear, the assignments gave me enough opportunity to practice."

Engaging and explains well

"The professor is very engaging and the lectures are well explained."

"This is a great course. Instructor is amazing and goes through a large number of examples."

Should remove "Data" from title

"The word "Data" must be removed from the course title.There is zero mentions of any form of data in the entirity of the course."

Not enough to prep for assessments

"The problem is the same for almost every course in this platform: Not enough material that can help students prepare better for the assessments, not enough examples in the lectures, the problems on the assessments cover material that was briefly mentioned during a lecture."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Calculus through Data & Modeling: Differentiation Rules with these activities:

Review the Product and Quotient Rules for Derivatives

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Strengthen your understanding of the Product and Quotient Rules, which will help you differentiate more complex functions.

Browse courses on Product Rule

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Review the mathematical formulas for the Product Rule and Quotient Rule.
Practice applying these rules to differentiate functions.

Practice Partial Derivatives

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Strengthen your ability to find partial derivatives, which are crucial for analyzing functions of multiple variables, often encountered in science and engineering.

Browse courses on Partial Derivatives

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Review the concept of partial derivatives.
Practice finding partial derivatives with respect to each variable.

Practice Derivatives of Trigonometric Functions

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Develop proficiency in finding derivatives of trigonometric functions, which are essential for analyzing periodic phenomena.

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Review the definitions of trigonometric functions.
Learn the differentiation formulas for sine, cosine, and tangent.
Practice applying these formulas to differentiate trigonometric functions.

Two other activities

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Tutorial on the Chain Rule

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Master the Chain Rule, a fundamental technique for differentiating composite functions, which are ubiquitous in real-world applications.

Browse courses on Chain Rule

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Watch video tutorials explaining the Chain Rule.
Follow step-by-step examples of applying the Chain Rule.
Practice using the Chain Rule to differentiate complex functions.

Practice Directional Derivatives and Gradient Vectors

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Develop your skills in finding directional derivatives and gradient vectors, which are essential for understanding the behavior of functions in multiple dimensions.

Browse courses on Directional Derivatives

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Review the concepts of directional derivatives and gradient vectors.
Practice calculating directional derivatives in different directions.
Practice finding gradient vectors and interpreting their geometric significance.

Career center

Learners who complete Calculus through Data & Modeling: Differentiation Rules will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists utilize statistical and computational techniques to extract insights from data. Calculus through Data & Modeling: Differentiation Rules would be highly beneficial for this role, as it provides a deep understanding of differentiation and its applications in data modeling. The course's emphasis on differentiation rules for various function types, such as polynomials, exponentials, logarithms, and trigonometric functions, would equip you with the skills to analyze and interpret complex data effectively.

See salaries and explore the career path for Data Scientist

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to assess risk and make investment decisions in the financial industry. Calculus through Data & Modeling: Differentiation Rules would be highly valuable for this role, as it provides a deep understanding of differentiation and its applications in financial modeling. The course's focus on differentiation rules for polynomial, exponential, and logarithmic functions is particularly relevant for analyzing financial data and developing trading strategies.

See salaries and explore the career path for Quantitative Analyst

Actuary

Actuaries leverage mathematical and statistical skills to assess risk and uncertainty. Calculus through Data & Modeling: Differentiation Rules would provide a solid foundation for this role by enhancing your understanding of derivatives and their applications in modeling and data analysis. The course's focus on differentiation rules, particularly those for polynomial, exponential, logarithmic, and trigonometric functions, would equip you with the necessary tools to calculate rates of change and approximate functions accurately.

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Statistician

Statisticians collect, analyze, and interpret data to draw meaningful conclusions. Calculus through Data & Modeling: Differentiation Rules would be highly beneficial for this role, as it provides a deep understanding of differentiation and its applications in statistical modeling. The course's focus on differentiation rules for various function types, such as polynomials, exponentials, logarithms, and trigonometric functions, would equip you with the skills to analyze and interpret complex data effectively.

See salaries and explore the career path for Statistician

Financial Analyst

Financial Analysts evaluate and forecast financial performance for businesses and investments. Calculus through Data & Modeling: Differentiation Rules would be highly relevant to this role, as it provides a strong foundation in differentiation and its applications in financial modeling. The course's focus on differentiation rules for polynomial, exponential, and logarithmic functions is particularly valuable for understanding and analyzing financial data and making informed investment decisions.

See salaries and explore the career path for Financial Analyst

Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to solve complex business problems. Calculus through Data & Modeling: Differentiation Rules would provide a strong foundation for this role, as it enhances your understanding of derivatives and their applications in modeling and optimization. The course's emphasis on differentiation rules for polynomial, exponential, and logarithmic functions would equip you with the skills to develop and analyze mathematical models that optimize business processes.

See salaries and explore the career path for Operations Research Analyst

Market Researcher

Market Researchers gather and analyze data to understand consumer behavior and market trends. Calculus through Data & Modeling: Differentiation Rules would be beneficial for this role, as it provides a solid understanding of differentiation and its applications in data analysis. The course's focus on differentiation rules for various function types, including polynomials, exponentials, logarithms, and trigonometric functions, would equip you with the skills to analyze and interpret market data effectively.

See salaries and explore the career path for Market Researcher

Business Analyst

Business Analysts use data and analysis to improve business processes and make informed decisions. Calculus through Data & Modeling: Differentiation Rules may be helpful in this role, as it provides a foundation in differentiation and its applications in data analysis. The course's emphasis on differentiation rules for polynomial, exponential, and logarithmic functions can be useful for understanding and analyzing business data.

See salaries and explore the career path for Business Analyst

Financial Manager

Financial Managers oversee the financial operations of organizations. Calculus through Data & Modeling: Differentiation Rules may be helpful in this role, as it provides a foundation in differentiation and its applications in financial analysis. The course's emphasis on differentiation rules for polynomial, exponential, and logarithmic functions can be useful for understanding and analyzing financial data.

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Investment Analyst

Investment Analysts evaluate and make recommendations on investment opportunities. Calculus through Data & Modeling: Differentiation Rules may be helpful in this role, as it provides a foundation in differentiation and its applications in financial analysis. The course's emphasis on differentiation rules for polynomial, exponential, and logarithmic functions can be useful for understanding and analyzing investment data.

See salaries and explore the career path for Investment Analyst

Epidemiologist

Epidemiologists investigate the causes and patterns of diseases in populations. Calculus through Data & Modeling: Differentiation Rules may be helpful in this role, as it provides a foundation in differentiation and its applications in data analysis. The course's emphasis on differentiation rules for polynomial, exponential, and logarithmic functions can be useful for understanding and analyzing epidemiological data.

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Risk Manager

Risk Managers assess and mitigate risks for organizations. Calculus through Data & Modeling: Differentiation Rules may be helpful in this role, as it provides a foundation in differentiation and its applications in data analysis. The course's emphasis on differentiation rules for polynomial, exponential, and logarithmic functions can be useful for understanding and analyzing risk data.

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Software Engineer

Software Engineers design, develop, and maintain software applications. Calculus through Data & Modeling: Differentiation Rules may be helpful in this role, as it provides a foundation in differentiation and its applications in computer science. The course's emphasis on differentiation rules for polynomial, exponential, and logarithmic functions can be useful for understanding and analyzing algorithms and data structures.

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Economist

Economists study and analyze economic data to understand economic trends and make policy recommendations. Calculus through Data & Modeling: Differentiation Rules may be helpful in this role, as it provides a foundation in differentiation and its applications in economic modeling. The course's emphasis on differentiation rules for polynomial, exponential, and logarithmic functions can be useful for understanding and analyzing economic data.

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Teacher

Teachers educate and inspire students at various levels. Calculus through Data & Modeling: Differentiation Rules may be helpful for this role, as it provides a deep understanding of differentiation and its applications in mathematics education. The course's focus on differentiation rules for various function types, such as polynomials, exponentials, logarithms, and trigonometric functions, can be useful for explaining these concepts to students effectively.

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