The difference between Derivative and Integral

When used as nouns, derivative means something derived, whereas integral means a number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.

When used as adjectives, derivative means obtained by derivation, whereas integral means constituting a whole together with other parts or factors.

check bellow for the other definitions of Derivative and Integral

  1. Derivative as an adjective:

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

    Examples:

    "a derivative conveyance; a derivative word"

  2. Derivative as an adjective:

    Imitative of the work of someone else.

  3. 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.

  4. Derivative as an adjective (finance):

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

  5. Derivative as an adjective:

    Lacking originality.

  1. Derivative as a noun:

    Something derived.

  2. Derivative as a noun (linguistics):

    A word that derives from another one.

  3. 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.

  4. Derivative as a noun (chemistry):

    A chemical derived from another.

  5. Derivative as a noun (calculus):

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

    Examples:

    "The derivative of <math>f:f(x) = x^2</math> is <math>f':f'(x) = 2x</math>"

  6. Derivative as a noun (calculus):

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

    Examples:

    "The derivative of <math>f(x) = x^2</math> at x = 3 is <math>f'(3) = 2 * 3 = 6</math>."

  1. Integral as an adjective:

    Constituting a whole together with other parts or factors; not omittable or removable

  2. Integral as an adjective (mathematics):

    Of, pertaining to, or being an integer.

  3. Integral as an adjective (mathematics):

    Relating to integration.

  4. Integral as an adjective (obsolete):

    Whole; undamaged.

  1. Integral as a noun (mathematics):

    A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.

    Examples:

    "The integral of <math>x\mapsto x^2</math> on <math>[0,1]</math> is <math>\frac{1}{3}</math>."

  2. Integral as a noun (mathematics):

    Antiderivative

    Examples:

    "The integral of <math>x^2</math> is <math>\frac{x^3}{3}</math> plus a constant."

Compare words:

Compare with synonyms and related words: