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Calculus through Data & Modeling

Differentiation Rules

Joseph W. Cutrone, PhD

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.

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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.

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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

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Reviews summary

Applied differentiation rules for data & engineering

According to students, this course offers a very solid foundation in differentiation rules, particularly for those looking to apply calculus in fields like data science and engineering. Learners frequently praise the clear explanations and step-by-step derivations of complex topics, including partial and directional derivatives. The practical examples and well-designed assignments, especially the final project on flight paths, are highlighted as effective for reinforcing understanding and demonstrating real-world application. While most find the pacing appropriate, some noted it might assume strong pre-existing knowledge. There is a mixed view on the depth of 'data & modeling' integration, with some finding it highly relevant and others expecting more pervasive integration.

Features well-designed assignments and a valuable capstone project.

"The final project on flight paths was a brilliant way to apply everything."

"The quizzes were fair... the assignments reinforced the learning effectively."

"The problem sets were challenging but fair, pushing me to think deeply."

"The assignments were well-designed to solidify understanding."

Emphasizes real-world applications, especially beneficial for career-focused learners.

"I really appreciated how they tied the concepts back to data modeling, which made it feel very relevant to my work."

"As an engineer, the application-focused approach was exactly what I needed."

"This course provided a fantastic foundation for understanding how calculus applies to real-world data problems."

"The practical examples were excellent. The course covers a lot of ground effectively."

Provides highly clear and practical explanations for complex calculus topics.

"The explanations were incredibly clear, especially on the chain rule and partial derivatives."

"The instructor explains complex topics like directional derivatives well."

"The instructor's passion for the subject shines through. I particularly enjoyed the clear breakdown of complex topics into manageable chunks."

"Exactly what I needed! Very clear explanations of differentiation rules and their applications."

May require a strong pre-existing calculus background for optimal understanding.

"My only minor gripe is that some of the earlier modules felt a bit rushed if you weren't already strong in pre-calculus..."

"The explanations were too fast, and I felt lost after the initial modules. It assumes a strong pre-existing knowledge of calculus."

"I struggled with this course... I was hoping for more foundational support."

The integration of data modeling varies in perceived depth and consistency.

"I expected a bit more 'data & modeling' integration throughout, not just in the final project."

"The 'data & modeling' aspect felt tacked on rather than integrated, which was disappointing for my career goals."

"Decent course, but it felt a bit like a standard calculus review rather than 'Calculus through Data & Modeling'."

"I really appreciated how they tied the concepts back to data modeling, which made it feel very relevant to my work."

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.

See salaries and explore the career path for Actuary

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

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

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.

See salaries and explore the career path for Financial Manager

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.

See salaries and explore the career path for Software Engineer

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.

See salaries and explore the career path for Economist

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.

See salaries and explore the career path for Epidemiologist

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.

See salaries and explore the career path for Risk Manager

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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Reading list

We've selected 14 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Calculus through Data & Modeling: Differentiation Rules.

Principles of Mathematical Analysis Textbook by...

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This classic textbook provides a rigorous introduction to mathematical analysis, including the foundations of differentiation and its applications.

Calculus through Data & Modeling

Differentiation Rules

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What's inside

Syllabus

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Reviews summary

Applied differentiation rules for data & engineering

Activities

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Reading list

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