Understanding mathematical concepts can be difficult, and one of the most confusing in Calculus is understanding the difference between differential and derivative. The two are closely related but cannot be used interchangeably; each one has its own distinct uses. In this blog post, we will take a deep dive into what makes them unique so you can gain a solid grasp on when to use either term. Whether you’re hoping to brush up on some terminology or learn more about derivatives and differentials for the first time, this post should give you all the information you need.

## What is Differential?

- Differential mathematics is a branch of applied mathematics that considers the behavior of functions and their derivatives with respect to changes in the independent variables. Differential mathematics relies on concepts such as limits, derivatives, approximations, and integration to analyze how a particular function behaves.
- Differential equations involve the study of physical systems that depend on differentiable functions for their properties. Differential mathematics forms an important part of modern engineering and physics, with its techniques being employed in many varied areas such as computational finance, machine learning, data science, and meteorology.
- Differential equations are also used heavily in models for population growth and epidemiological research. Differential mathematics is a complex but powerful tool that has become increasingly important throughout many scientific disciplines.

## What is Derivative?

- A derivative is a fundamental mathematical concept relating to the idea of finding the rate of change of one quantity with respect to another. Derivatives are represented by symbols called differential operator symbols (represented ∂), and a Derivative is calculated by showing the region being affected in relation to a particular aspect.
- Derivatives have applications in many areas such as statistics, economics, physics, and chemistry, or just about any other field which involves collecting and analyzing data.
- Derivatives can be used to construct complicated equations, or simply used as an analytical tool in order to understand and interpret data more effectively. Derivatives can reveal patterns and trends that may otherwise not be visible without this type of analysis.

## Difference between Differential and Derivative

Differential and derivative are two related mathematical concepts that are often confused, but they are distinct from one another. Differentials measure the rate of change between the output and the input of a process, while derivatives measure the rate of change of the outputs that result from small changes in input.

- Differentials provide a general measure, whereas derivatives require more information such as a specific point or boundary, and can produce more accurate results.
- Differential equations attempt to find answers to issues involving a change in some variable over time, while derivatives attempt to predict how one variable will react when other variables in a problem are changed.
- Differentials and derivatives are incredibly important components of mathematics, helping scientists understand and predict certain occurrences in nature.

## Conclusion

The terms differential and derivative are often used interchangeably, but they actually have different meanings. A differential is a small change in a variable, while a derivative is the rate of change of a function with respect to one of its variables. In calculus, derivatives are used to calculate tangents and slopes, whereas equations involving differentials are used to approximate functions. When working with derivatives and differentials, it’s important to be aware of the difference between them so that you can use the correct term in each situation.