Applications of Differential Calculus

Differential calculus has lots of applications in domains such as physics, engineering, economics and biology. Some of the common use cases are:

Rate of Change: Determining how quickly a quantity is changing over time, space, or another variable.
Optimization: Finding maximum or minimum values of functions, which is useful in optimizing processes or resources.
Curve Sketching: Analyzing the behavior of functions, including identifying critical points, inflection points, and concavity.
Physics: Calculating velocity, acceleration, and other kinematic properties of moving objects.
Economics: Modeling marginal cost, marginal revenue, and profit functions in business and economics.
Biology: Describing population growth and decay, enzyme kinetics, and other biological processes.
Engineering: Analyzing stress and strain in materials, designing structures, and optimizing systems.
Finance: Determining interest rates, analyzing investment portfolios, and modeling financial derivatives.
Computer Graphics: Generating smooth curves and surfaces, such as in 3D modeling and animation.

Fundamental of Differential Calculus

Differential calculus is a branch of calculus that studies the concept of a derivative and its applications. Derivative tells us about the rate at which a function changes at any given point. Differential Calculus is crucial to many scientific and engineering areas since it allows for the estimation of instantaneous rates of change and curve slopes. In this article, we will be discussing about Differential Calculus and its fundamentals, which every students should know.

This article helps learners in understanding of differential calculus, its concepts, and its applications. By the end of this article, readers should be able to understand the fundamentals of derivatives and use them to solve real-world issues.

Table of Content

Key Concepts in Differential Calculus

Limits
Continuity
Derivatives:
Differentiation Notation

Basic Rules of Differentiation

Product Rule of Derivative
Quotient Rule of Derivatives
Sum Rule of Derivative
Power Rule of Derivative
Constant Multiple Rule of Derivative
Chain Rule of Derivative