Differentiation Rules - Power Laws, Polynomials, Quotients, and Reciprocals - Generalized Power Rule

Generalized Power Rule

The elementary power rule generalizes considerably. The most general power rule is the functional power rule: for any functions f and g,

wherever both sides are well defined.

Special cases:

  • If f(x) = xa, f′(x) = axa − 1 when a is any real number and x is positive.
  • The reciprocal rule may be derived as the special case where g(x) = −1.

Read more about this topic:  Differentiation Rules, Power Laws, Polynomials, Quotients, and Reciprocals

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