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:
“...every woman who has any margin of time or money to spare should adopt some one public interest, some philanthropic undertaking, or some social agitation of reform, and give to that cause whatever time and work she may be able to afford ...”
—Frances Power Cobbe (1822–1904)
“Better the rule of One, whom all obey,
Than to let clamorous demagogues betray
Our freedom with the kiss of anarchy.”
—Oscar Wilde (1854–1900)