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:
“Sometimes, because of its immediacy, television produces a kind of electronic parable. Berlin, for instance, on the day the Wall was opened. Rostropovich was playing his cello by the Wall that no longer cast a shadow, and a million East Berliners were thronging to the West to shop with an allowance given them by West German banks! At that moment the whole world saw how materialism had lost its awesome historic power and become a shopping list.”
—John Berger (b. 1926)
“Freedom prospers when religion is vibrant and the rule of law under God is acknowledged.”
—Ronald Reagan (b. 1911)