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2. Product rule - Wikipedia

   en.wikipedia.org/wiki/Product_rule

   In calculus, the product rule (or Leibniz rule [1] or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions.For two functions, it may be stated in Lagrange's notation as () ′ = ′ + ′ or in Leibniz's notation as () = +.

3. Differentiation rules - Wikipedia

   en.wikipedia.org/wiki/Differentiation_rules

   Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative. [ citation needed ] Logarithms can be used to remove exponents, convert products into sums, and convert division into subtraction — each of which may lead to a simplified ...

4. Matrix calculus - Wikipedia

   en.wikipedia.org/wiki/Matrix_calculus

   In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces 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 entities.

5. Derivative - Wikipedia

   en.wikipedia.org/wiki/Derivative

   Another common notation for differentiation is by using the prime mark in the symbol of a function ⁠ ⁠. This is known as prime notation , due to Joseph-Louis Lagrange . [ 22 ] The first derivative is written as ⁠ f ′ ( x ) {\displaystyle f'(x)} ⁠ , read as " ⁠ f {\displaystyle f} ⁠ prime of ⁠ x {\displaystyle x} ⁠ , or ⁠ y ...

6. List of formulas in Riemannian geometry - Wikipedia

   en.wikipedia.org/wiki/List_of_formulas_in...

   This is a list of formulas encountered in Riemannian geometry. Einstein notation is used throughout this article. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise.

7. Vector calculus identities - Wikipedia

   en.wikipedia.org/wiki/Vector_calculus_identities

   2.3 Product rule for multiplication by a ... Similar rules apply to algebraic and differentiation formulas. For algebraic formulas one may alternatively use the left ...

8. General Leibniz rule - Wikipedia

   en.wikipedia.org/wiki/General_Leibniz_rule

   The proof of the general Leibniz rule [2]: 68–69 proceeds by induction. Let and be -times differentiable functions.The base case when = claims that: ′ = ′ + ′, which is the usual product rule and is known to be true.

9. Generalizations of the derivative - Wikipedia

   en.wikipedia.org/wiki/Generalizations_of_the...

   The Carlitz derivative is an operation similar to usual differentiation but with the usual context of real or complex numbers changed to local fields of positive characteristic in the form of formal Laurent series with coefficients in some finite field F q (it is known that any local field of positive characteristic is isomorphic to a Laurent ...