First Derivative (Noun)
Meaning
The result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx.
Classification
Nouns denoting cognitive processes and contents.
Examples
- The first derivative of a function represents the rate of change of the function's output with respect to one of its variables.
- To find the maximum or minimum of a function, we need to find the point where the first derivative equals zero.
- The first derivative of the position function gives the velocity function, which describes the rate of change of an object's position.
- In calculus, the first derivative is used to determine the slope of a tangent line to a curve at a given point.
- The first derivative test is a method used to determine whether a critical point of a function is a local maximum, minimum, or neither.