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 = x a, f x = ax a 1 when a is any nonzero real number and x is positive.; The reciprocal rule may be derived as the special case where g x = 1..In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially overes of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single en.ies..Common Derivatives and Integrals Visit//tutorial.math.lamar.edu for a complete set of Calculus I II notes. 2005 Paul Dawkins Inverse Trig Functions 1.Provided the derivative is known to exist. It should be noted that the above definitions refer to "real" derivatives, i.e., derivatives which are restricted to directions along the real axis.However, this restriction is artificial, and derivatives are most naturally defined in the complex plane, where they are sometimes explicitly referred to as complex derivatives..
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Differentiation Rules Wikipedia
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 = x a, f x = ax a 1 when a is any nonzero real number and x is positive.; The reciprocal rule may be derived as the special case where g x = 1..

Matrix Calculus Wikipedia
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially overes of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single en.ies..

Nn Cx Ncx Nn Lamar University
Common Derivatives and Integrals Visit//tutorial.math.lamar.edu for a complete set of Calculus I II notes. 2005 Paul Dawkins Inverse Trig Functions 1.

Derivative From Wolfram Mathworld
Provided the derivative is known to exist. It should be noted that the above definitions refer to "real" derivatives, i.e., derivatives which are restricted to directions along the real axis.However, this restriction is artificial, and derivatives are most naturally defined in the complex plane, where they are sometimes explicitly referred to as complex derivatives..