Differentiation and Integration: The Two Pillars of Advanced Mathematics

Calculus can be defined as one of the most important mathematics topics; this topic of mathematics is taught to students in higher classes and in colleges for the students who want to pursue their careers in engineering. Calculus is the most advanced topic to be used in everyday mathematics. It is one of the most ancient branches of mathematics and a topic that students usually find very difficult. Still, with constant practice and hard work, this topic can be easily mastered upon. In calculus, students usually study differentiation and the use of differentiation formula and integration to find out the area of the curve and many other things.

This article deals with differentiation and integration, which are the basics of calculus. This article also stresses the tips on how to remember the differentiation formulas for a longer period.

First of all, let’s see what differentiation and integration are about.

Differentiation is generally carried out to break down the given function into various parts, and integration is done to unite those parts in which the function was broken to form the original function. The differentiation and integration formula is geometrically carried out to find the slope of a given curve and the area of the given curve, respectively.

Listed below is the list of formulas that we use in differentiation and integration.

1) Implicit differentiation formula:

This formula of differentiation is finding a derivative of an implicit equation concerning the variable we desire, that is x. There is no formula to differentiate these implicit functions; thus, we will have to use chain rule while differentiating an implicit function.

2) U V Formula:

UV Differentiation formula is a very useful formula in differentiation. The UV formula carried out with the help differentiation is the addition of the derivative of the first function, which is multiplied with the second function keeping the second function constant, and the differentiation of the second function, which is multiplied with the first function without differentiating it.

3) Product rule:

Product rule in mathematics is a formula that one can use to take out the derivatives of two or more mathematics functions.

The product rule supports us in taking out the derivative of two differentiable functions that are being multiplied together by combining the ability of both the power rule and the addition and subtraction rule for derivatives.

These are some of the most important formulas which we study in mathematics. There are some more formulas like the higher derivative formula and logarithmic formula, which are also used in calculus.

Listed below are some of the tips which one must keep in mind while learning the differentiation and integration formula and remembering it for a longer period.

• One needs to make a shortlist of all the formulas on one single page and try to write it with different colors, if possible. This will help in easily revising the formula.
• One needs to revise formulas every day until one feels that he has mastered it, and there is no chance that he will forget.
• While solving the questions, one needs to write the formula which is used in the particular question; this will make the mind brush up and remember the formula constantly.
• One needs to carry out a self-test every day. Either writing can do this down all the formulas or by giving an oral test.
• It has also been observed that if one tries to remember the formula in connection with something that one always remembers, it will help ease learning.

These are some of the tips that should be kept in mind while learning differentiation and integration formulas.

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