Sentence examples for derivative exists from inspiring English sources

A function is differentiable at t if its derivative exists for that specific value of t.

It is differentiable if the derivative exists for all t for which f(t) is defined.

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.

If the (finite) right-hand derivative exists, then (1.19).

Hence, we can see that Caputo' s derivative is defined for functions for which Riemann-Liouville fractional order derivative exists.

Let F be continuously differentiable and suppose that the second derivative exists throughout an open convex set (Usubseteq V).

A function f is said to be Δ-differentiable if its Δ-derivative exists.

We say that f is (Delta_{H} -differentiable at t if its (Delta_{H} -differentiablests at t.

Moreover, we say that f is (Delta_{H} -differentiable on (matH} -differentiable (Delta_{H})-derivative exists at each (tinmathbb{T}^{k}).

If D gH X ( t 0 ) ∈ I n satisfying (2.4) exists, we say that X is generalized Hukuhara differentiable (gH-differentiable for short) at t 0. Let us remark that the gH-derivative exists at t 0 if and only if the left and right derivatives at t 0 exist and they are equal.

satisfies (1.2) for, ; the one-sided derivatives exist at (resp., ), ; the one-sided second-order derivatives exist at (resp., ),.