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.MSC 2010: 26A24, 05A30, 41A58arXiv:1705.02516Keywords: Quantum calculus, Quantum algebra, Power quantum calculus, Quantum difference, q-derivative, Jackson derivative, q-calculus, q-difference, Time Scale Calculus, Series Expansion, Taylor's theorem, Taylor's formula, Taylor's series, Taylor's polynomial, Analytic function, Series representation, Derivative, Differential calculus, Difference Equations, Numerical Differentiation, Polynomial, Exponential function, Exponentiation, Binomial coefficient, Binomial theorem, Binomial expansion, Mathematics, Numerical analysis, Mathematical analysis, arXiv, Preprint