cho f(x)= logx (x+2) tính f'(x) bằng bao nhiêu a. 0

* Hướng dẫn giải

Đáp án C

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)={\log }_{\mathrm{x}}(\mathrm{x}+2)=\frac{\ln (\mathrm{x}+2)}{\mathrm{lnx}} \\ \Rightarrow \mathrm{f}\text{'}\left(\mathrm{x}\right)=\frac{{\displaystyle \frac{1}{\mathrm{x}+2}}\mathrm{lnx}-\ln (\mathrm{x}+2).{\displaystyle \frac{1}{\mathrm{x}}}}{{\ln }^2\mathrm{x}}=\frac{\mathrm{xlnx}-(\mathrm{x}+2)\ln (\mathrm{x}+2)}{\mathrm{x}(\mathrm{x}+2){\ln }^2\mathrm{x}} \\ \Rightarrow \mathrm{f}\text{'}\left(2\right)=\frac{2\ln 2-4\ln 4}{8{\ln }^{2}2}=\frac{-6\ln 2}{8{\ln }^{2}2}=\frac{-3}{4\ln 2} \end{gathered}$$