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In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards."
The tangent half-angle substitution relates an angle to the slope of a line. Introducing a new variable = , sines and cosines can be expressed as rational functions of , and can be expressed as the product of and a rational function of , as follows: = +, = +, = +.
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 ...
Download QR code; Print/export Download as PDF; ... Pages in category "Differentiation rules" The following 11 pages are in this category, out of 11 total.
Considering in particular the set in R n where the v-directional derivative of u fails to exist (which must be proved to be measurable), the latter condition is met due to the one-dimensional case of Rademacher's theorem. The second step of Morrey's proof establishes the linear dependence of the v-directional derivative of u upon v. This is ...
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 () = +.
Excel 2.0 for Windows, which was modeled after its Mac GUI-based counterpart, indirectly expanded the installed base of the then-nascent Windows environment. Excel 2.0 was released a month before Windows 2.0, and the installed base of Windows was so low at that point in 1987 that Microsoft had to bundle a runtime version of Windows 1.0 with ...
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = (), where both f and g are differentiable and ()