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What is Differentiation

What is Differentiation?

Learn about What is Differentiation?

In calculus, have you heard about the term ‘derivatives’ ?. No!. Let me tell you, derivatives are the rate that changes with respect to any other quantity i.e. time. For example, acceleration is defined as the rate of change in velocity with respect to the time taken. Differentiation can be defined as the process by which we can find the function of a derivative. There are various laws related to the differential formulas, these laws were provided or given by a great scientist ‘Sir Issac Newton’. These laws are applicable in various disciplines of science and mathematics. The maximum or minimum value of the velocity or the rate of acceleration is determined by the help of differential formulas. In this article, we will try to cover some basic aspects of differentiation such as differentiation formulas, linear and nonlinear equations, and different types of notations and do a detailed analysis about them.

The History of Differentiation

The concept of derivatives with respect to a tangent line was evolved very early. These terms are generally regarded by the time when famous geometers ( those who study geometry ) such as Archimedes, Euclids, and the Apollonius who is also known as the Apollonius of Perga. These concepts were primarily used to calculate the volumes and area of various geometrical shapes. If we talk about our own country i.e. In India, the use of infinitesimals was used in the contrary of differential formulas. It was first used by the Great Indian Mathematician, ‘Aryabhatta’ to study the orbit of the moon around 500 A.D.  Bhaskara II who is known from the Shaka era made significant and vital developments in the area to compute the rate of changes. Many important terms and notions of calculus can also be found with the help of Rolle’s theorem. The modern calculus that you study today was developed with the help of scientists such as Sir Issac Newton and Gottfried Wilhelm Leibniz from 1646 to 1716. They were the one who provided the unified and independent notation for differentiation and derivatives.

Some Significant Applications of Differential Formulas

As mentioned above,  differentiation can be defined as the process by which we can find the function of a derivative. The use of differentiation has been widely used in the worlds of physics and mathematics. The following points analyses some significant and vital applications of differentiations and their formulas.

  • The differentiation formulas are used to find the rate and value of acceleration. The term ‘acceleration’ can be defined as the rate of change in velocity with respect to the time given. It is always measured in the units of meters per second square units.
  • Have you ever observed a graph with the highest points and lowest points which is also known as the curves of a graph. These points are calculated with the help of differential formulas.
  • It is also used to determine the value of the tangent of a curve. The tangent of a circle can be defined as the line or a point that touches a curve of a circle.

What is the Formula of Differentiation?

The formulas which help to calculate any sum regarding differentiation and its equations can be defined as the differentiation formulas. It includes trigonometric function ( sine, cosine, tangent, cotangent, secant, and cosecant) logarithmic function, basic function which includes linear and nonlinear functions. These formulas are based on various rules such as sum rule, product rule, quotient rule, and chain rule. We shall look at the history and origin of the modern and old differentiation formula and some of its applications.

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