Mathematics for Business Studies - Differentiation Rules and Derivatives
Learn the rules of differentiation and the derivatives of inverse trigonometric functions in this free online course.Publisher: ADU
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Differentiation Rules and Derivatives is a free online course from Alison that outlines the method used in the rules of differentiation and derivatives of inverse trigonometric functions. You will be taught the expansion of a Binomial in addition to the application and the proof of the power rule. Study the applications and methods used to prove keeping a multiplicative constant rule. You will be introduced to the application, along with the proof of the sum and difference rule. Learn about the application as well as the proof of the Product Rule. Solutions to problems involving the quotient rule will also be provided in this course. Explore the derivations and examples of the sine function as well as the solution to problems using the cosine function. Learn about the derivatives of other trigonometric functions. Scholars who take this course will acquire the knowledge of the construct and applications of a composite function in addition to the proof of the chain rule.
Do you seek to gain a proper understanding of the application of implicit functions and implicit differentiation? Then this course is for you. Learn about the application and the procedure used for differentiating a parametrized curve. Study the method of differentiating implicitly defined functions in addition to the solution to mathematical problems of the higher-order derivatives. You will learn about the derivation and application of the arcsine in addition to the arctangent functions. You will be taught the derivation and application of the remaining inverse functions. Study the derivatives of logarithmic functions together with how to graph a logarithm function. Learn about the derivative of ln x along with the derivative of the log of x. Students will gain an understanding of the procedure of finding derivatives using logarithmic differentiation. Learn about the application and method of finding the derivatives of exponential functions. You will study the applications of the derivative of in motion problems as well as in business and economics. Study the optimization or min/max problems in addition to related rate problems.
Lastly, an optimization problem seeks an optimal value for a variable quantity, y, which depends on another variable quantity, x, over which we have control. There are conditions, also known as constraints, that limit our choice of values for x. The so-called optimal value of y can be a maximum or a minimum. This course will use real-world examples to explain and solve optimization problems. You will be taught the application and analysis of linear approximations. You will also learn about the concept, summary, and application of differentials. Taking this course will lay out the foundation for the concept and graphing of derivatives using Newton's method. You will study the various parts and applications of L'Hopital's rule. This course will be of great benefit to learners, students, researchers in business mathematics, commercial enterprises, business majors, and all who have an interest in mathematics for business studies. Register for this course today and begin your next learning journey!Start Course Now
Rules of Differentiation
Rules of Differentiation - Learning Outcomes
The Power Rule
The Sum and Difference Rule
Derivatives of Trigonometric Functions
Composite Functions and the Chain Rule
Rules of Differentiation - Lesson Summary
Derivatives of Inverse Trigonometric Functions
Derivatives of Inverse Trigonometric Functions - Learning Outcomes
Inverse Trigonometric Functions
Derivatives of Logarithmic Functions
Applications of the Derivative
Derivatives of Inverse Trigonometric Functions - Lesson Summary
Upon successful completion of this course, you will be able to:
- Analyze the expansion of a Binomial and the proof of the power rule.
- Discuss the application, along with the proof of major differentiation rules.
- Analyze the derivations of trigonometric functions.
- Describe the constructs and applications of a composite function.
- Analyze the application of implicit functions and implicit differentiation.
- Describe the derivatives of logarithmic functions.
- Outline the procedure of finding derivatives using logarithmic differentiation.
- Analyze the applications of the derivative of in real-world problems.
- Discuss the application and analysis of linear approximations.
- Discuss the concept of derivatives using Newton's method and the various parts of L'Hopital's rule.
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