Cho hàm số \(y=f\left(x\right)=\dfrac{\cos x}{1+2\sin x}\). Khẳng định nào trong các khẳng định sau là sai?
\(f'\left(\dfrac{\pi}{2}\right)=-\dfrac{1}{3}\).\(f'\left(-\dfrac{\pi}{2}\right)=-1\).\(f'\left(\dfrac{\pi}{6}\right)=-\dfrac{5}{4}\).\(f'\left(0\right)=-2\).Hướng dẫn giải:\(f'\left(x\right)=\left(\dfrac{\cos x}{1+2\sin x}\right)'=\dfrac{\left(\cos x\right)'\left(1+2\sin x\right)-\cos x.\left(1+2\sin x\right)'}{\left(1+2\sin x\right)^2}=\dfrac{-\sin x\left(1+2\sin x\right)-\cos x.\left(2\cos x\right)}{\left(1+2\sin x\right)^2}=\dfrac{-2-\sin x}{\left(1+2\sin x\right)^2}\)
\(f'\left(\dfrac{\pi}{2}\right)=-\dfrac{1}{3}\); \(f'\left(-\dfrac{\pi}{2}\right)=-1\); \(f'\left(\dfrac{\pi}{6}\right)=-\dfrac{5}{8}\) \(f'\left(0\right)=-2\); Khẳng định sai là \(f'\left(\dfrac{\pi}{6}\right)=-\dfrac{5}{4}\)
