Đạo hàm của hàm số $\large y = \left(\dfrac{1}{2}\right)^{x^2+1}$ là:

Đạo hàm của hàm số $\large y = \left(\dfrac{1}{2}\right)^{x^2+1}$ là: 

• A.

  $\large 2x.\ln\dfrac{1}{2}$

• B.

  $\large (x^2+1)\left(\dfrac{1}{2}\right)^{x^2+1}$

• C.

  $\large 2x.\left(\dfrac{1}{2}\right)^{x^2}.\ln 2$

• D.

  $\large -x.\left(\dfrac{1}{2} \right )^{x^2}.\ln2$

Chọn D

Ta có: 

$\large y = \left(\dfrac{1}{2} \right )^{x^2+1}\Rightarrow y'= \left[\left(\dfrac{1}{2} \right ) ^{x^2+1}\right ]'= (x^2+1)'\left(\dfrac{1}{2} \right )^{x^2+1}.\ln\left(\dfrac{1}{2} \right )=2x.\dfrac{1}{2}\left(\dfrac{1}{2} \right )^{x^2}.\ln 2^{-1}=-x.\left(\dfrac{1}{2} \right )^{x^2}.\ln2$