Cho hàm số y = f(x) 

C

- Hướng dẫn giải

Đáp án C

Ta có $f\text{'}\left(x\right)=-e^x.f^2\left(x\right)\iff \frac{f\text{'}\left(x\right)}{f^2\left(x\right)}=-e^x\iff \int \frac{f\text{'}\left(x\right)}{f^2\left(x\right)}dx=\int -e^{x}dx=\int \frac{d\left(f\left(x\right)\right)}{f^2\left(x\right)}dx=-e^x+C$

$\iff -\frac{1}{f\left(x\right)}=-e^x+C\iff f\left(x\right)=\frac{1}{e^x-C}$ mà $f\left(0\right)=\frac{1}{2}\Rightarrow \frac{1}{1-C}=\frac{1}{2}\Rightarrow C=-1$ 

Vậy $f\left(x\right)=\frac{1}{e^x+1}\Rightarrow f\left(\ln 2\right)=\frac{1}{e^{\ln 2}+1}=\frac{1}{2+1}=\frac{1}{3}$.