Tìm đạo hàm của các hàm số sau : 

$$\begin{gathered} a, y=2\sqrt{x}\sin x-\frac{\cos }{x}; b,y=\frac{3\cos }{2x+1} ; c, y=\frac{t^2+2\mathrm{co}st}{\sin t} \\ d, y=\frac{2\mathrm{co}s\phi -\sin \phi }{3\sin \phi +\cos \phi }; e, y=\frac{\tan x }{\sin x+2} f,y=\frac{cotx}{2\sqrt{x}-1} \end{gathered}$$

Giải

$$\begin{gathered} a, y\text{'}=\frac{\left(\sqrt{x}+1\right)x\sin x+\left(2x^2\sqrt{x}+1\right)\cos x }{x^2} \\ b,y\text{'}=\frac{-3\left(2x+1\right)\sin x-6\mathrm{co}sx}{{\left(2x+1\right)}^2} \\ c,y\text{'}=\frac{2t\sin t-t^2\cos t-2 }{{\sin }^{2}t} \\ d, y\text{'}=\frac{-7}{{\left(3\sin \phi +\cos \phi \right)}^2} \\ e,y\text{'}=\frac{2+{\sin }^{3}x}{{\cos }^{2}x{\left({\sin }^{2}x+2\right)}^2} \\ f.y\text{'}=\frac{{\displaystyle \frac{1-2\sqrt{x}}{{\sin }^{2}x}}-{\displaystyle \frac{cotx }{\sqrt{x}}}}{{\left(2\sqrt{x}-1\right)}^2} \end{gathered}$$