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The rate of change is usually with respect to time. Because science and engineering often relate quantities to each other, the methods of related rates have broad applications in these fields. Differentiation with respect to time or one of the other variables requires application of the chain rule, [1] since most problems involve several variables.
The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.
In calculus, the constant of integration, often denoted by (or ), is a constant term added to an antiderivative of a function () to indicate that the indefinite integral of () (i.e., the set of all antiderivatives of ()), on a connected domain, is only defined up to an additive constant.
Since the derivative of ln(x) is 1 / x , one makes (ln(x)) part u; since the antiderivative of 1 / x 2 is − 1 / x , one makes 1 / x 2 part v. The formula now yields: The formula now yields:
The Cauchy formula for repeated integration, namely () = ()! (), leads in a straightforward way to a generalization for real n: using the gamma function to remove the discrete nature of the factorial function gives us a natural candidate for applications of the fractional integral operator as () = () ().
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
What is a 1.35 factor rate?A 1.35 factor rate is a mid-range rate lenders charge to borrow money. Factor rates typically fall between 1.1 and 1.5. With a 1.35 factor rate, it will cost $35,000 to ...
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.