Tìm đạo hàm cả hàm số $\Large y=\dfrac{\log2x}{x^2}$ A. $\Large y'=\df

Tìm đạo hàm cả hàm số $\Large y=\dfrac{\log2x}{x^2}$

• A.

  A. $\Large y'=\dfrac{1-4.\ln2x}{2x^3\ln10}$

• B.

  B. $\Large y'=\dfrac{1}{2x^2\ln10}$

• C.

  C. $\Large y'=\dfrac{1-2\ln2x}{x^3\ln10}$

• D.

  D. $\Large y'=\dfrac{1-2\log2x}{x^3}$

Chọn C

ADCT: $\Large \log_{a}x=\dfrac{\ln x}{\ln a}; (\log_{a}x)'=\dfrac{1}{x.\ln a}$

$\Large y'=\dfrac{(\log 2x)'.x^2-(x^2)'.\log2x}{x^4}=\dfrac{\left(\dfrac{1}{x.\ln10}\right).x^2-2x.\log2x}{x^4}$$\Large =\dfrac{\dfrac{x}{\ln10}-\dfrac{2x.\ln2x}{\ln10}}{x^4}=\dfrac{1-2\ln2x}{x^3.\ln10}$