## 6 Conclusions  
The present research study aims to develop a reliable and sensitive analytical method for the quantitative determination of five antioxidant drugs in a cold cream prepared in the laboratory. Purification conditions for the quantitative recovery of the analytes from the cream substrate were decided based on an experimental design methodology. The method was efficient, easy to operate, and short enough to be applied in routine analyses. A corresponding method was successfully used to study the transdermal penetration of the five drugs (in cream and suspension) with vertical Franz cells. Based on the results, the APIs act synergistically since their degree of penetration into the skin is different, ensuring an overall better antioxidant regenerative effect on the skin. The overall effort is expected to yield new insights into the field of anti-aging cosmetics. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Amount of Drug in Suspension**} & \multicolumn{6}{c}{**Amount of Drug in Cream**} \\ \hline  & \multicolumn{2}{c}{**Reference Sample**} & \multicolumn{2}{c}{**Donor**} & \multicolumn{2}{c}{**Acceptor**} & \multicolumn{2}{c}{**Membrane**} & \multicolumn{2}{c}{**Reference Sample**} & \multicolumn{2}{c}{**Donor**} & \multicolumn{2}{c}{**Acceptor**} & \multicolumn{2}{c}{**Membrane**} \\ \cline{2-11}
**Drug** & **Loaded** & **Found** & **Loaded** & **Final** & **Final** & **Leaded** & **Found** & **Loaded** & **Final** & **Final** \\  & **(\%)** & **(\%)** & **Sample** & **Found** & **Found** & **(\%)** & **(\%)** & **Sample** & **Found** & **Found** \\ \hline RTN & 750.0 & 337.5 & 750.0 & - & 315.2 & 2040.0 & 2092.5 & 2040.0 & - & 1875.8 \\ \(\alpha\)-TOC & 5000.0 & 1887.5 & 5000.0 & - & 1988.6 & 639.1 & 6590.0 & 639.1 & 5765.7 \\ RSV & 2600.0 & 545.0 & 2600.0 & 169.8 & 3494.4 & 33253.3 & 3163.0 & 3235.3 & 155.5 & 2693.8 \\ FERA & 1300.0 & 565.0 & 1300.0 & 432.4 & 31.5 & 1641.6 & 1426.3 & 1641.6 & 397.7 & 726.2 \\ QR & 2500.0 & 2232.5 & 2500.0 & - & 2132.3 & 3417.0 & 3652.5 & 3417.0 & 22.7 & 2871.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Amounts of APIs loaded and found in the reference sample (cold cream and suspension), in the donor, and acceptor chambers and in the membrane tissue. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**J (\(\text{ug}/\text{cm}^{2}/\text{h}\))**} & \multicolumn{3}{c}{**P\({}_{\text{app}}\) (h/\(\text{cm}^{2}\)) \(\times\) 10\({}^{-3}\)**} \\ \cline{2-7}
**Cell** & **FERA** & **RSV** & **QR** & **FERA** & **RSV** & **QR** \\ \hline Cream & 2.344 \(\pm\) 0.131 & 3.276 \(\pm\) 0.674 & 1.890 \(\pm\) 0.339 & 0.455 \(\pm\) 0.026 & 0.323 \(\pm\) 0.066 & 0.188 \(\pm\) 0.034 \\ \hline Solution & 3.303 \(\pm\) 0.801 & 4.466 \(\pm\) 0.566 & - & 0.578 \(\pm\) 0.135 & 0.315 \(\pm\) 0.065 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Steady-state flux Jss and P\({}_{\text{app}}\) coefficient values for ferulic acid, resveratrol, and quercetin. **Supplementary Materials:** The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app142411843/s1](https://www.mdpi.com/article/10.3390/app142411843/s1)]([https://www.mdpi.com/article/10.3390/app142411843/s1](https://www.mdpi.com/article/10.3390/app142411843/s1)), Figure S1: Chromatographic separation of the five substances in (A) phenyl and (B) C18 columns at 290, 370, 326 and 320 nm; Table S1: Physicochemical properties of the studied compounds; Figure S2: Chromatograms (at 290 nm) of three different mobile phases with acetonitrile/water 50:50 \(v/v\) and (1) formic acid 0.2% (FA), (2) acetic acid 0.2% (ACA) and (3) trifluoroacetic acid 0.1% (TFA); Figure S3: Ultraviolet (UV) spectra of the analytes; Figure S4: Chromatogram of the five substances at different wavelengths and Blank sample chromatogram; Figure S5: Chromatogram of resveratrol in the formulation (tR = 8.6 min); Figure S6: Residue plots of the five substances; Figure S7: Diagram of the superposition of the isometric curves.