Title: On the quantum differentiation of smooth real-valued functions,
Abstract: Calculating the value of $C^{k\in\{1,\infty\}}$ class of smoothness
real-valued function's derivative in point of $\mathbb{R}^+$ in radius of
convergence of its Taylor polynomial (or series), applying an analog of
Newton's binomial theorem and $q$-difference operator. $(P,q)$-power difference
introduced in section 5. Additionally, by means of Newton's interpolation
formula, the discrete analog of Taylor series, interpolation using
$q$-difference and $p,q$-power difference is shown.