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Bài tập 107 trang 133 SGK Toán 12 NC

Bài tập 107 trang 133 SGK Toán 12 NC

Đối với hàm số \(y = \ln \frac{1}{{x + 1}}\), ta có:

(A) \({xy' + 1 = {e^y}}\)

(B) \({xy' + 1 =  - {e^y}}\)

(C) \({xy' - 1 = {e^y}}\)

(D) \({xy' - 1 =  - {e^y}}\)

 

ADSENSE

Hướng dẫn giải chi tiết

\(\begin{array}{l}
y =  - \ln \left( {x + 1} \right) \Rightarrow y' =  - \frac{1}{{x + 1}}\\
 \Rightarrow xy' + 1 = x.\frac{{ - 1}}{{x + 1}} + 1\\
 = \frac{{ - x}}{{x + 1}} + 1 = \frac{1}{{x + 1}} = {e^y}
\end{array}\)

Chọn (A).

-- Mod Toán 12 HỌC247

 
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