In mathematics, the power rule is one of the most important differentiation rules in calculus. Since differentiation is linear, polynomials can be differentiated using this rule.
The power rule holds for all powers except for the constant value which is covered by the constant rule. The derivative is just rather than which is undefined when .
The inverse of the power rule enables all powers of a variable except to be integrated. This integral is called Cavalieri's quadrature formula and was first found in a geometric form by Bonaventura Cavalieri for . It is considered the first general theorem of calculus to be discovered.
This is an indefinite integral where is the arbitrary constant of integration.
The integration of requires a separate rule.
Hence, the derivative of is and the integral of is .
Read more about Power Rule: Power Rule, Differentiation of Arbitrary Polynomials, Generalizations
Famous quotes containing the words power and/or rule:
“Poetry is above all a concentration of the power of language, which is the power of our ultimate relationship to everything in the universe.”
—Adrienne Rich (b. 1929)
“The principle of majority rule is the mildest form in which the force of numbers can be exercised. It is a pacific substitute for civil war in which the opposing armies are counted and the victory is awarded to the larger before any blood is shed. Except in the sacred tests of democracy and in the incantations of the orators, we hardly take the trouble to pretend that the rule of the majority is not at bottom a rule of force.”
—Walter Lippmann (1889–1974)