\cdot \frac{d\left(2^{x}\right)}{d\left(3^{x}\right)}=\left(\frac{2}{3}\right)^{x}\frac{2^{x-1}}{3^{x-1}}\left(\frac{2}{3}\right)^{x} \log _{3} 2\left(\frac{2}{3}\right)^{x} \log _{2} 3\left(\frac{2}{3}\right)^{x} \log _{3} 2$
\cdot \frac{d\left(2^{x}\right)}{d\left(3^{x}\right)}=\left(\frac{2}{3}\right)^{x}\frac{2^{x-1}}{3^{x-1}}\left(\frac{2}{3}\right)^{x} \log _{3} 2\left(\frac{2}{3}\right)^{x} \log _{2} 3$
\cdot \frac{d\left(2^{x}\right)}{d\left(3^{x}\right)}=\left(\frac{2}{3}\right)^{x}\frac{2^{x-1}}{3^{x-1}}\left(\frac{2}{3}\right)^{x} \log _{3} 2\left(\frac{2}{3}\right)^{x} \log _{2} 3$