This is the second course after Calculus 1: Differentiation and Integration: Lines and Curves already published here on Udemy. In this course, we illustrate the application of three rules of differentiation: Chain, Product and Quotient rules to logarithmic functions.
In the first course we illustrated the application of basic differentiation to linear and polynomial functions i.e., we differentiated sums and differences of simple polynomial functions and here we illustrate the differentiation of products and quotients of logarithmic functions. To benefit more from this course, we recommend that you buy both courses together.
In keeping with our unconventional approach we use the unorthodox method or approach to teaching where we do not teach concepts directly from a set text book but we answer particular questions that have appeared in past examination papers and teach and illustrate the application of concepts.
So in essence these courses are best for students of mathematics who are aware of the concepts already but are interested in seeing them being applied in the answering of practical questions in order to boost their confidence in understanding and applying these concepts to answer real world questions.
Learning concepts is easy but applying them could be a night mare unless if one practices and practices and practices. These courses help you just do that. The questions are answered during a shooting session to simulate what students under exam conditions go through. Mistakes are made and corrected on the go so you are aware that mistakes do happen but that should not destruct you from pressing on.
Two questions are answered in this course. The first one to illustrate the use of the chain rule and product rule using a logarithmic function of a product of two functions a root and a cubic function. Three alternative approaches to doing so are presented in 3 lectures to cater for students at different levels of development.
The second question illustrates the application of the chain rule and quotient rule in answering a question involving the logarithm of a quotient of linear functions. The real question requires us to find the equations of a tangent and its normal at a point on the logarithmic function. Very similar to what we did in the first course only that we were then dealing with linear and polynomial functions instead of exponents and logarithmic functions.
The chain rule is the most versatile and most powerful method of differentiation. Also known as differentiation by substitution it is the differentiation of a function of a function in which you differentiate the outside function first ( in our case here the logarithmic function) and multiply the result to the differentiation of the inner function (here either a product or a quotient of two other functions). It is a beautiful method.
The product rule illustrates how a product of two functions is differentiated and the quotient rule illustrates how a quotient of two functions is differentiated.
The application to finding the equation of a tangent and its normal at a particular point on the logarithmic function is classical and can be appreciated more here with prior experience of its use as illustrated in our first course: Calculus 1: Differentiation and Integration: Lines and Curves.
You might be wondering where and how all this is applied in real work situations? Follow through the courses and in no time you will appreciate these building blocks.
