FIRST DERIVATIVE Meaning and
Definition
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The first derivative, also known as the derivative, signifies a fundamental concept in calculus and mathematics at large. It refers to the rate of change of a function at any given point on its graph. Mathematically speaking, the first derivative of a function f(x) denoted as f'(x) or dy/dx, expresses the instantaneous rate of change, or the slope of a tangent line, at a specific point on the graph.
To obtain the first derivative, one must apply the rules of differentiation, such as the power rule or the chain rule, to the original function. This process allows the determination of how the function's values change with respect to the independent variable. The resulting first derivative provides essential information regarding the behavior of the function, including the existence of maximum and minimum values, inflection points, and the concavity of the graph.
Apart from aiding in the interpretation of graphs and understanding the behavior of functions, the first derivative is extensively used in various scientific and practical applications. For instance, it is employed in physics to calculate velocities and accelerations, in economics to determine marginal rates and elasticity, in optimization to find maximum or minimum points, and in differential equations to solve various mathematical models.
Overall, the first derivative is a crucial mathematical tool that provides insights into the behavior and characteristics of functions, enabling the analysis of change and aiding in the formulation of mathematical models applicable to numerous disciplines.
Common Misspellings for FIRST DERIVATIVE
- dirst derivative
- cirst derivative
- virst derivative
- girst derivative
- tirst derivative
- rirst derivative
- furst derivative
- fjrst derivative
- fkrst derivative
- forst derivative
- f9rst derivative
- f8rst derivative
- fiest derivative
- fidst derivative
- fifst derivative
- fitst derivative
- fi5st derivative
- fi4st derivative
- firat derivative
Etymology of FIRST DERIVATIVE
The etymology of the word "first derivative" can be traced back to Latin and Greek roots. The term "derivative" comes from the Latin word "derivare", which means "to lead or draw off". In mathematics, a derivative indicates the rate at which a specified dependent quantity changes with respect to an independent variable.
The word "first" is derived from the Old English word "fyrest", which means "foremost or earliest". In the context of calculus, the "first derivative" refers to the rate of change of a function at a specific point, or the slope of the tangent line at that point.
Therefore, the term "first derivative" combines the Latin and Old English roots to describe the initial or primary measure of change in a function with respect to the independent variable.
Similar spelling word for FIRST DERIVATIVE
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