Calculus is a branch of mathematics that focuses on the calculation of the instantaneous rate of change (differentiation) and the sum of infinitely small pieces to determine the object as a whole (integration). Two popular mathematicians Newton and Gottfried Wilhelm Leibniz developed the concept of calculus in the 17^{th} century.

Today, this is the basic entry point for students who want to learn chemistry, physics, science, economics, or finance etc. If you wanted to calculate the position of the space shuttle from shuttle then it is possible through calculus even the problem is complex or quite difficult. These days there are a plenty of computer tools that can be used to solve the calculus problem in minutes.

The process of finding derivatives or instantaneous rate of change with respect to a function, it is termed as differentiation. In contrast, this is possible to carry out differentiation by real algebraic manipulations, rules of operations, and the information on how to manipulate functions.

Differentiation is a technique to measure the rate of change for curves, graphs, images, etc. You can determine the tangent or slope along a given direction.With this process, you can also check where the lower and upper values occur. The early applications of differentiation in calculus include planetary motion, gravity, ship design, fluid flow, geometrical shapes, and bridge engineering etc.

Take an example of the small curve whose slope or tangent is difficult to calculate without the right technique. Here, we had to use a list of basic differentiation formulas to make the process easier. You can also calculate the average rate of change over the longer time intervals where actual speed is difficult to determine without proper formulas.

Partial derivatives in the mathematics of a function of multiple variables are its derivatives with respect to those variables. Partial derivatives are used for vectors and many other things like space, motion, differential geometry etc.

The derivatives are used to calculate the slope of a function at any given point. There are differentiation rules that can be used in different conditions as per the requirement. They are tough to understand at a first glance, So, you need a proper understanding of the rules before you actually implement them for the complex problems.

The applications of derivatives in real-life are just the endless and they can be utilized in almost every sector like physics, chemical engineering, science, space, differential geometry, ship design, fluid flow, bridge manufacturing, and many more. These are some practical examples where differentiation formulas are needed to calculate the slope or tangent of a function.

Other than this, differentiation formulas can also be used for the preparation of competitive exams, and higher studies. They are taken an important part of the curriculum and need continuous practice to solve tough problems. They sound difficult if you don’t any in-depth understanding of differentiation formulas. SO, they are necessary to learn by students during schools and colleges etc.