Mathematics for Business Studies - Differentiation Rules and Derivatives

This course 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. 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. Learners who complete all the modules 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 want a proper understanding of the application of implicit functions and implicit differentiation? 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 are 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 uses 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 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 students of business mathematics and all who have an interest in math for business studies.