Question

$\mathrm{If}y=\left(\begin{array}{ccc}\sin x& \cos x& \sin x\\ \cos x& -\sin x& \cos x\\ x& 1& 1\end{array}\right|,\mathrm{then}\frac{\mathrm{dy}}{\mathrm{dx}}=$ .

• A. -1
• B. cos 2x
• C. 0.0
• D. 1

Answer 1

The correct option is D 1

$\frac{\mathrm{dy}}{\mathrm{dx}}=\left(\begin{array}{ccc}\cos x& -\sin x& \cos x\\ \cos x& -\sin x& \cos x\\ x& 1& 1\end{array}\right|+\left(\begin{array}{ccc}\sin x& \cos x& \sin x\\ -\sin x& -\cos x& -\sin x\\ x& 1& 1\end{array}\right|+\left(\begin{array}{ccc}\sin x& \cos x& \sin x\\ \cos x& -\sin x& \cos x\\ 1& 0& 0\end{array}\right|=0-\left(\begin{array}{ccc}\sin x& \cos x& \sin x\\ \sin x& \cos x& \sin x\\ x& 1& 1\end{array}\right|+\left(\begin{array}{cc}\cos x& \sin x\\ -\sin x& \cos x\end{array}\right|=0-0+{\cos }^{2}x+{\sin }^{2}x=1$