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In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
This is a list of Latin words with derivatives in English language. Ancient orthography did not distinguish between i and j or between u and v. [1] Many modern works distinguish u from v but not i from j. In this article, both distinctions are shown as they are helpful when tracing the origin of English words. See also Latin phonology and ...
Derivative (chemistry), a type of compound which is a product of the process of derivatization Derivative (linguistics), the process of forming a new word on the basis of an existing word, e.g. happiness and unhappy from happy
In chemistry, a derivative is a compound that is derived from a similar compound by a chemical reaction.. In the past, derivative also meant a compound that can be imagined to arise from another compound, if one atom or group of atoms is replaced with another atom or group of atoms, [1] but modern chemical language now uses the term structural analog for this meaning, thus eliminating ambiguity.
More generally, the differential or pushforward refers to the derivative of a map between smooth manifolds and the pushforward operations it defines. The differential is also used to define the dual concept of pullback. Stochastic calculus provides a notion of stochastic differential and an associated calculus for stochastic processes.
for the first derivative, for the second derivative, for the third derivative, and for the nth derivative. When f is a function of several variables, it is common to use "∂", a stylized cursive lower-case d, rather than "D". As above, the subscripts denote the derivatives that are being taken.
Similarly, the derivative of the second derivative, if it exists, is written f ′′′ and is called the third derivative of f. Continuing this process, one can define, if it exists, the n th derivative as the derivative of the (n-1) th derivative. These repeated derivatives are called higher-order derivatives.
Morphological derivation, in linguistics, is the process of forming a new word from an existing word, often by adding a prefix or suffix, such as un-or -ness. For example, unhappy and happiness derive from the root word happy.