In finance, a derivative contract is one whose value is derived from that of one or more underlying securities, commodities or other quantities such as the weather.
A derivative work is a modification of an original work, such as a book, a play, a movie a musical composition, etc. For example, movie based on a novel is a derivative work.
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The derivative of a function at a certain point is a measure of the rate at which that function is changing as an argument undergoes change.
Derivatives are defined by taking the limit of the slope of secant lines as they approach a tangent line.
If the second derivative is positive at a critical point, that point is a local minimum; if negative, it is a local maximum; if zero, it may or may not be a local minimum or local maximum.
Points on the graph of a function where the derivative is undefined or equals zero are called critical points or sometimes stationary points (in the case where the derivative equals zero).
Acceleration is the derivative (with respect to time) of an object's velocity, that is, the second derivative (with respect to time) of an object's position.
The common thread is that the derivative at a point serves as a linear approximation of the function at that point.
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