What is the purpose of differentiation in mathematics?
The Definition of Differentiation. The essence of calculus is the derivative. The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point.
The derivative measures the steepness of the graph of a function at some particular point on the graph. Thus, the derivative is a slope. (That means that it is a ratio of change in the value of the function to change in the independent variable.)
- In mathematics, the derivative is a way to show rate of change: that is, the amount by which a function is changing at one given point. For functions that act on the real numbers, it is the slope of the tangent line at a point on a graph.
- Unlike the indefinite integral, which represents a function, the definite integral represents a number, and is simply the signed area under the curve of f.
- Concavity. The second derivative of a function f measures the concavity of the graph of f. A function whose second derivative is positive will be concave up (also referred to as convex), meaning that the tangent line will lie below the graph of the function.
Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. For example, in physics, calculus is used in a lot of its concepts.
- The following topics are presented with applications in the business world: functions, graphs, limits, exponential and logarithmic functions, differentiation, integration, techniques and applications of integration, partial derivatives, optimization, and the calculus of several variables.
- Gottfried Wilhelm Leibniz
- Differential Calculus deals with the concept of taking a derivative, also called differentiation. This means take really small parts of a line to find the slope of a curve at every point. Integral Calculus deals with taking the Integral of a curve, also called integrating.
Updated: 6th December 2019