It is differentiable if the derivative exists for all t for which f(t) is defined.
A function is differentiable at t if its derivative exists for that specific value of t.
f is nondecreasing with respect to the functional variable and, and. the derivatives, exist on E and, for t ∈ [0, a], for each x ∈ [-b, b] the functions, are absolutely continuous.
satisfies (1.2) for, ; the one-sided derivatives exist at (resp., ), ; the one-sided second-order derivatives exist at (resp., ),.
We investigate the functions spaces on for which the generalized partial derivatives exist and belong to different Lorentz spaces, where and is nonincreasing and satisfies some special conditions.
(x t)) is continuous on (mathbb{R}^); the derivative (x'(t)) exists for (tinmathbb{R}^) with the possible exception of the points (theta_{k}), (kinmathbb{N}), where one-sided derivatives exist; (5) is satisfied by (x t)) on each interval ((theta_{k},theta_{k+1})), (kinmathbb{N}), and it holds for the right derivative of (x t)) at the points (theta_{k}), (kinmathbb{N}).
Since the derivation function of s n ( x ) is a polynomial, all of the derivatives must exist for all real numbers.
These findings suggest that curcumin derivatives exist predominantly in the enol form during binding to Aβ aggregates, and that the enolization of curcumin derivatives is crucial for binding to Aβ aggregates.
Cauchy discovered that, if a function's first derivative exists, then all its derivatives exist, and therefore it can be represented by a power series in z its Taylor series.
For the sake of convenience, assume that all the integrals and all the derivatives exist.
