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, fâ˛(x) = axa â 1 when a is any real number and x is positive.
- The reciprocal rule may be derived as the special case where g(x) = â1.
Read more about this topic: Differentiation Rules, Power Laws, Polynomials, Quotients, and Reciprocals
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