  In a 2006 article (\cite{A1}), Allouba gave his quadratic covariation
differentiation theory for It\^o's integral calculus. He defined the derivative
of a semimartingale with respect to a Brownian motion as the time derivative of
their quadratic covariation and a generalization thereof. He then obtained a
systematic differentiation theory containing a fundamental theorem of
stochastic calculus relating this derivative to It\^o's integral, a
differential stochastic chain rule, a differential stochastic mean value
theorem, and other differentiation rules. Here, we use this differentiation
theory to obtain variants of the Clark-Ocone and Stroock formulas, with and
without change of measure. We prove our variants of the Clark-Ocone formula
under $L^{2}$-type conditions; with no Malliavin calculus, without the use of
weak distributional or Radon-Nikodym type derivatives, and without the
significant machinery of the Hida-Malliavin calculus. Unlike Malliavin or
Hida-Malliavin calculi, the form of our variant of the Clark-Ocone formula
under change of measure is as simple as it is under no change of measure, and
without requiring any further differentiability conditions on the Girsanov
transform integrand beyond Novikov's condition. This is due to the invariance
under change of measure of the first author's derivative in \cite{A1}. The
formulations and proofs are natural applications of the differentiation theory
in \cite{A1} and standard It\^o integral calculus. Iterating our Clark-Ocone
formula, we obtain variants of Stroock's formula. We illustrate the
applicability of these formulas by easily, and without Hida-Malliavin methods,
obtaining the representation of the Brownian indicator
$F=\mathbb{I}_{[K,\infty)}(W_{T})$, which is not standard Malliavin
differentiable, and by applying them to digital options in finance. We then
identify the chaos expansion of the Brownian indicator.
