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v. t. e. In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function 's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
The derivatives in the table above are for when the range of the inverse secant is [,] and when the range of the inverse cosecant is [,]. It is common to additionally define an inverse tangent function with two arguments , arctan ( y , x ) . {\displaystyle \arctan(y,x).}
Calculus. In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. [1][2][3] Let , where both f and g are differentiable and The quotient rule states that the derivative of h(x) is. It is provable in many ways by using other derivative rules.
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4.The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1.
Wolfram Language. The Wolfram Language (/ ˈwʊlfrəm / WUUL-frəm) is a proprietary, [7] general, very high-level multi-paradigm programming language [8] developed by Wolfram Research. It emphasizes symbolic computation, functional programming, and rule-based programming [9] and can employ arbitrary structures and data. [9] It is the ...
WolframAlpha (/ ˈwʊlf.rəm -/ WUULf-rəm-) is an answer engine developed by Wolfram Research. [3] It is offered as an online service that answers factual queries by computing answers from externally sourced data. [4][5] WolframAlpha was released on May 18, 2009, and is based on Wolfram's earlier product Wolfram Mathematica, a technical ...
The total derivative is a linear combination of linear functionals and hence is itself a linear functional. The evaluation measures how much points in the direction determined by at , and this direction is the gradient. This point of view makes the total derivative an instance of the exterior derivative. Suppose now that is a vector-valued ...
www.stephenwolfram.com. twitter.com /stephen _wolfram. Stephen Wolfram (/ ˈwʊlfrəm / WUUL-frəm; born 29 August 1959) is a British-American [6] computer scientist, physicist, and businessman. He is known for his work in computer algebra, and theoretical physics. [7][8] In 2012, he was named a fellow of the American Mathematical Society.
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