Cho hàm...

C

- Hướng dẫn giải

Chọn C

$f^{\text{'}}\left(x\right)=\frac{-2\cos x\sin x\left(1+{\sin }^{2}x\right)-2\cos x\sin x{\cos }^{2}x}{{\left(1+{\sin }^{2}x\right)}^2}$

$\begin{array}{l}=\frac{-2\cos x\sin x\left(1+{\sin }^{2}x+{\cos }^{2}x\right)}{{\left(1+{\sin }^{2}x\right)}^2}\\ =\frac{-4\cos x\sin x}{{\left(1+{\sin }^{2}x\right)}^2}\end{array}$

$\Rightarrow f^{\text{'}}\left(\frac{\pi }{4}\right)=\frac{-8}{9}$