- $y' = {e^x}\left( {\frac{1}{{\ln x}} - \frac{1}{{x{{\ln }^2}x}}} \right)$
- $y' = {e^x}\left( {1 + \frac{1}{{x\ln x}}} \right)$
- $y' = {e^x}\left( {\frac{1}{{\ln x}} + \frac{1}{{x{{\ln }^2}x}}} \right)$
- $y' = {e^x}\left( {1 - \frac{1}{{x\ln x}}} \right)$