Hàm số y=(sinx-xcosx)/(cosx+xsinx) có đạo hàm bằng

* Hướng dẫn giải

Chọn D

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