Search results
Results from the WOW.Com Content Network
By a slight change in notation (and viewpoint), for an interval [ a, b ], the difference quotient. is called [5] the mean (or average) value of the derivative of f over the interval [ a, b ]. This name is justified by the mean value theorem, which states that for a differentiable function f, its derivative fⲠreaches its mean value at some ...
Numerical differentiation. Finite difference estimation of derivative. In numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.
A finite difference is a mathematical expression of the form f (x + b) â f (x + a).If a finite difference is divided by b â a, one gets a difference quotient.The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.
Differentiation is linear. The product rule. The chain rule. The inverse function rule. Power laws, polynomials, quotients, and reciprocals. The polynomial or elementary power rule. The reciprocal rule. The quotient rule. Generalized power rule.
For a given arbitrary stencil points of length with the order of derivatives , the finite difference coefficients can be obtained by solving the linear equations [5] where is the Kronecker delta, equal to one if , and zero otherwise. Example, for , order of differentiation :
Symmetric derivative. In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative. It is defined as: [1] [2] The expression under the limit is sometimes called the symmetric difference quotient. [3] [4] A function is said to be symmetrically differentiable at a point x if its symmetric derivative exists at that ...
Divided differences. In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. [citation needed] Charles Babbage 's difference engine, an early mechanical calculator, was designed to use this algorithm in its operation. [1]
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 .