Cho f(x)=logx(x+2) . Tính f'(x) a. f'(2)=-3/4 ln2 B. f'(x)=0

* Hướng dẫn giải

Đáp án A

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