in math⌗

The derivative measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

For example, the derivative of the position of a moving object with respect to time is the object’s velocity: this measures how quickly the position of the object changes when time advances.

The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.

in linguistics⌗

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 -ness or un-. For example, happiness and unhappy derive from the root word happy.

This is contrasted with inflection, in that derivation produces a new word (a distinct lexeme), whereas inflection produces grammatical variants of the same word.

in law⌗

A derivative work is an expressive creation that includes major copyright-protected elements of an original, previously created first work (the underlying work). The derivative work becomes a second, separate work independent in form from the first.

A shareholder derivative suit is a lawsuit brought by a shareholder on behalf of a corporation against a third party. Often, the third party is an insider of the corporation, such as an executive officer or director.

in finance⌗

A complex financial instrument formally known as a derivative security is a contract that derives its value from the performance of an underlying entity. Such an instrument has a value that changes non-linearly in relation to a primary asset or variable, such as interest rate, commodity price, credit rating, or foreign exchange rate.

in chemistry⌗

Derivatization is a technique used in analytical chemistry to synthesize a small change of chemical structure via a simple reaction. The original chemical compound converts to a similar, but distinct, structure. The technique is used in gas chromatography, mass spectrometry, and various other processes.

More fundamentally, organic compounds are found to naturally derive from other, more complex compounds. Of particular importance to living organisms are the nucleotides found in cells, which are derivatives of the compounds purine and pyrimidine. Four of the five major nucleotide bases - commonly abbreviated A, G, T, C - arrange into sequences tens of millions of nucleotides long by linking the phosphate molecule of one to a carbon molecule in the next. Two such polymer strands are wound together into a double helix, DNA, and determines the structure of proteins synthesized within a cell.

Proteins form the internal machinery within brain cells and the connective tissue between brain cells. They also control the chemical reactions that allow brain cells to communicate with each other. These so-called neurotransmitters give rise to the behaviors and processes that we associate with consciousness within the psyche.