Cho ham số y=f(x)=cosx/(1+2sinx) tính f'(x)

* Hướng dẫn giải

Chọn  B

$\begin{array}{l}f\text{'}\left(x\right)=\frac{-\sin x.\left(1+2\sin x\right)-\cos x\mathrm{.2.}\cos x}{{\left(1+2\sin x\right)}^2}\\ =\frac{-\mathrm{s}{\text{inx - 2sin}}^{2}x-2c{\text{os}}^{2}x}{{(1+2\sin x)}^2}\\ =\frac{-\mathrm{s}\text{inx}-2({\sin }^{2}x+\text{}c{\text{os}}^{2}x)}{{(1\text{}+2\sin x)}^2}\\ =\frac{-\sin x-2}{{\left(1+2\sin x\right)}^2}\end{array}$