differentiable function


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differentiable function

[‚dif·ə′ren·chə·bəl ′fəŋk·shən]
(mathematics)
A function which has a derivative at each point of its domain.
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Suppose that f : [a, b] [right arrow] R be a twice differentiable function on (a,b) and suppose that [gamma] [less than or equal to] f" (t) [less than or equal to] [GAMMA] for all t [member of] (a, b).
The method allows receiving the mathematical description difficult nonlinear and even piecewise dependence in the form of unitary continuously differentiable function with any accuracy of approach allowed by data.
Let x(t)[member of]R be a continuous and differentiable function.
1] are differentiable functions on M, then M is said to be a generalized complex space form (see [13] and [14]).
If we also define a differentiable error function of the network outputs such as the sum-of-square error function, then the error function itself is a differentiable function of the weights.
which is a variant of Simpson's inequality for first differentiable function f, [f.
Levine [1,2]) Let [PSI](t) be a positive, twice differentiable function which satisfies for t> 0, the inequality
where a(Y) is an unknown, continuous, positive, and differentiable function.
d] and 0 < q [less than or equal to] + [infinity], if there exists an infinitely differentiable function [eta] satisfying [eta]([xi]) = 1 if [absolute value of [xi]] [less than or equal to] [rho] and [eta]([xi]) = 2[rho] for some 0 < p < 1/2 such that jz([eta]v)/w) belongs to [L.
n-k,] and a continuously differentiable function h : V [right arrow] W with continuously differentiable inverse such that