Differentiation

Consider the following statements

Statement 1 : If \(y=\log _{10} x+\log _e x\), then \(\frac{d y}{d x}=\frac{\log _{10} e}{x}+\frac{1}{x}\)

Statement 2 : If \(\frac{d}{d x}\left(\log _{10} x\right)=\frac{\log x}{\log 10}\) and \(\frac{d}{d x}\left(\log _e x\right)=\frac{\log x}{\log e}\)