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This is a list of limits for common functions such as elementary functions. ... All differentiation rules can also be reframed as rules involving limits.
Table of common limits; Table of derivatives; Table of integrals; Table of mathematical symbols; List of integrals; List of integrals of rational functions; List of integrals of irrational functions; List of integrals of trigonometric functions; List of integrals of inverse trigonometric functions; List of integrals of hyperbolic functions
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 ...
Limits describe the behavior of a function at a certain input in terms of its values at nearby inputs. They capture small-scale behavior using the intrinsic structure of the real number system (as a metric space with the least-upper-bound property). In this treatment, calculus is a collection of techniques for manipulating certain limits.
The process of finding a derivative is called differentiation. There are multiple different notations for differentiation, two of the most commonly used being Leibniz notation and prime notation. Leibniz notation, named after Gottfried Wilhelm Leibniz , is represented as the ratio of two differentials , whereas prime notation is written by ...
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This states that differentiation is the reverse process to integration. Differentiation has applications in nearly all quantitative disciplines. In physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of the velocity with respect to time is acceleration.
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