Sentence examples for derivatives exist from inspiring English sources

The existence of the total derivative f′('a') is strictly stronger than the existence of all the partial derivatives, but if the partial derivatives exist and are continuous, then the total derivative exists, is given by the Jacobian, and depends continuously on 'a'a

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.

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

Note that, this implies that the one-sided derivatives exist at.

For the sake of convenience, assume that all the integrals and all the derivatives exist.

Besides the already described compound serinol (2-amino-1,3-propanediol), several chiral derivatives exist.

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.

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

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

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