The difference between Derivative and Radical

Derivative as an adjective:

Obtained by derivation; not radical, original, or fundamental.

Derivative as an adjective:

Imitative of the work of someone else.

Derivative as an adjective (legal, copyright):

Referring to a work, such as a translation or adaptation, based on another work that may be subject to copyright restrictions.

Derivative as an adjective (finance):

Having a value that depends on an underlying asset of variable value.

Derivative as an adjective:

Lacking originality.

Derivative as a noun:

Something derived.

Derivative as a noun (linguistics):

A word that derives from another one.

Derivative as a noun (finance):

A financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc.

Derivative as a noun (chemistry):

A chemical derived from another.

Derivative as a noun (calculus):

The derived function of a function (the slope at a certain point on some curve f(x))

Derivative as a noun (calculus):

The value of this function for a given value of its independent variable.

Radical as an adjective:

Favoring fundamental change, or change at the root cause of a matter.

Radical as an adjective (botany, not comparable):

Pertaining to a root .

Radical as an adjective:

Pertaining to the basic or intrinsic nature of something.

Radical as an adjective:

Thoroughgoing; far-reaching.

Radical as an adjective (lexicography, not comparable):

Of or pertaining to the root of a word.

Radical as an adjective (phonology, phonetics, not comparable, of a sound):

Produced using the root of the tongue.

Radical as an adjective (chemistry, not comparable):

Involving free radicals.

Radical as an adjective (math):

Relating to a radix or mathematical root.

Radical as an adjective (slang, 1980s & 1990s):

Excellent; awesome.

Radical as a noun (historical: 19th-century Britain):

A member of the most progressive wing of the Liberal Party; someone favouring social reform (but generally stopping short of socialism).

Radical as a noun (historical: early 20th-century France):

A member of an influential, centrist political party favouring moderate social reform, a republican constitution, and secular politics.

Radical as a noun:

A person with radical opinions.

Radical as a noun (arithmetic):

A root (of a number or quantity).

Radical as a noun (linguistics):

In logographic writing systems such as the Chinese writing system, the portion of a character (if any) that provides an indication of its meaning, as opposed to phonetic.

Radical as a noun (linguistics):

In Semitic languages, any one of the set of consonants (typically three) that make up a root.

Radical as a noun (chemistry):

A group of atoms, joined by covalent bonds, that take part in reactions as a single unit.

Radical as a noun (organic chemistry):

A free radical.

Radical as a noun (algebra, commutative algebra, ring theory, of an [[ideal]]):

Given an ideal I in a commutative ring R, another ideal, denoted Rad(I) or \sqrt{I}, such that an element x ∈ R is in Rad(I) if, for some positive integer n, xn ∈ I; equivalently, the intersection of all prime ideals containing I.

Radical as a noun (algebra, ring theory, of a [[ring]]):

Given a ring R, an ideal containing elements of R that share a property considered, in some sense, "not good".

Radical as a noun (algebra, ring theory, of a [[module]]):

The intersection of maximal submodules of a given module.

Radical as a noun (number theory):

The product of the distinct prime factors of a given positive integer.