Q. If $y = \sin^{n}\ x\cos{nx,}then\frac{dy\ }{dx}\$is
A) ${n\ \sin}^{n - 1}\ x\sin(n + 1)x$
B) ${n\ \sin}^{n - 1}\ x\cos(n - 1)x$
C) $n{\ sin}^{n - 1}\ x\cos{nx}$
D) $n{\ sin}^{n - 1}\ x\cos(n + 1)x$
Explanation
(d)
Given, $y = \sin^{n}{x\cos{nx}}$
$\frac{dy}{dx} = n\sin^{n - 1}{x\cos{x\cos{nx - n\ \sin^{n}\ x\sin{nx}}}}\ \$
= $n\sin^{n - 1}{x\lbrack\cos x\cos{nx - \sin{x\sin{nx\rbrack}}}}$
= $n\sin^{n - 1}{x\cos{(n + 1)\ x}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.