One of the topics which seems to be a tough challenge for most senior secondary schools students is Calculus. Some students don’t even want to hear you say dy/dx in the classroom because they often describe it as “difficult”.
In this article, I will explicitly explain in details the concept of differentiation and also an elementary integration which will be useful for candidates who are about to sit for the upcoming Senior Schools Certificate Examinations.
CALCULUS ( Derivatives)
Basically the concept of differentiation describes a process for obtaining an expression which shows the rate of change of a given function. This concept finds a very large application in physics , economics, engineering and many other specializations.
The simple formula for finding the derivative of a function y is given as:
The above formula is derived through a process know of first principles. But for this scope we shall not go into how to prove it in this article.
Product Rule: If y=uv , where u and v are both functions of x, then:
You might be a little bit surprised how the derivate of the number (1) in the example above became zero.
Here is a proof to show that the differentiation of ordinary numbers which we can call constant (k) is always zero:
Quotient Rule: If y=u/v where both u and v are functions of x, then:
Chain Rule: This is another important rule in differentiation which is also called function of a function rule. If y=f(z) where z is a function of x. Then:
Trigonometric Differentiation: When we find the derivates of trigonometric functions using the first principles and applying appropriate trig identity where necessary, the following results will be obtained:
It is advisable to be familiar with these results to speed up your work. We shall talk about how to prove it in another article, “kindly click on the follow button on this page to get updates from me. “
Before, I move to integration, I will leave you with this class exercise which I expect you to solve and tell me the answer in the comment section. Here are the questions:
This is the reverse process of differentiation. It is often called anti-derivative .
Here is the basic formula for solving integral problems:
These two examples above are indefinite integral, we also have definite integral.
But because of time, we shall end today’s class here , to get update on when I post the continuation article, kindly click on the follow button at the top right corner.
I’ll be here to entertain questions and expect solution to the class work on what we’ve learnt.