# Differentiation Formula: Read Useful Information Here!

In mathematics, we generally define derivatives as the value changing with respect to the variable. The derivative formula is used to find the functions of the derivatives and these formulas used in the lower or elementary functions can be defined as the **differentiation formula**. In a constant function, the derivative is generally remembered as 0 if y is equivalent to k, where k is the constant in the differentiation formula, thus y is also regarded as 0. These formulas range from trigonometric functions to logarithmic functions and also basic functions. This topic is considered one of the toughest in mathematics but it is not so. In this article, we may try to cover various aspects of differentiation and do a brief analysis about them.

## Differentiation

In mathematics, you might have studied the topic calculus, it is something that most probably covers every aspect of geometry in higher studies. Differentiation is one of the branches of calculus and plays a very major and significant role in the fundamental operation of calculus. The other way or you can say the simplest way of defining differentiation is that it is a process of finding the continuous functions of derivatives. The most common and basic example is the rate of change in the shortest distance ( displacement ) with respect to the time taken which is called velocity.

## Some Real-Life Applications Of Differentiation

In the few paragraphs mentioned above, we studied differentiation and its formula with detailed analysis in respect of mathematics. But, there are various other applications of differentiation in the world of physics. The following point mentioned below analyses the real-life applications or uses of differentiation;

- The changing of the rate in the velocity with respect to the time taken is defined as acceleration which is denoted by the small letter ‘a’ having the standard unit of meter per second square. We can get to know about acceleration just because of differentiation.
- We know that differentiation is a process of finding the continuous functions of derivatives, this is known as the derivative function. In order to know the initial or terminal and highest or lowest point or the turning point in a coordinate graph, the derivative functions come to work.
- You might have heard about the term tangent, it is a horizontal or vertical line that touches the circle at a fixed point but never crosses it. Thus, differentiation is used to find out the tangent and the normal to a curve.
- The derivative functions are also used in order to find the profit and loss of running industry or business using some bar graphs. They are also used to check the variation in the temperature. It also comes to work in order to derive some serious equations in physics.
- This also comes to work in order to find the resultant standard unit of various rates such as velocity and speed or distance. For example; miles per hour covered, kilometer per hour or meter per second, and various others.

## Linear Functions And Nonlinear Functions

A linear function can be defined as the overall rate of change in the function with a constant rate through the help of its domain. The rate of change or the changing rate is different in the case of nonlinear functions. These two differ due to the nature of the function. This rate of change in the function can be regarded or defined as the function of derivatives. Thus, we can conclude that the nature of variation is parallel to that of the nature of the function.

If you want to learn about differentiation in a detailed manner, in a fun way, and in an interesting manner, you may visit the website of Cuemath and understand math the Cuemath way.