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In differential calculus, there is no single uniform notation for differentiation. Instead, various notations for the derivative of a function or variable have been proposed by various mathematicians. The usefulness of each notation varies with the context, and it is sometimes advantageous to use more than one notation in a given context.
In single-variable calculus, the difference quotient is usually the name for the expression ... By a slight change in notation (and viewpoint), for an interval ...
The concept of limit also appears in the definition of the derivative: in the calculus of one variable, this is the limiting value of the slope of secant lines to the graph of a function. History [ edit ]
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to 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.
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
In calculus, the differential represents the principal part of the change in a function = with respect to changes in the independent variable. The differential is defined by = ′ (), where ′ is the derivative of f with respect to , and is an additional real variable (so that is a function of and ).
Lagrange's notation for the derivative: If f is a function of a single variable, ′, read as "f prime", is the derivative of f with respect to this variable. The second derivative is the derivative of f ′ {\displaystyle f'} , and is denoted f ″ {\displaystyle f''} .
This glossary of calculus is a list of definitions about ... in Leibniz's notation in the following way. If a variable z depends ... of a single variable, ...
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