Search any question & find its solution
Question:
Answered & Verified by Expert
If $y=\sin ^{n} x \cos n x$, then $\frac{d y}{d x}$ is
Options:
Solution:
2864 Upvotes
Verified Answer
The correct answer is:
$n \sin ^{n-1} x \cos (n+1) x$
Given, $\mathrm{y}=\sin ^{\mathrm{n}} \mathrm{x} \cos \mathrm{nx}$
$$
\begin{aligned}
\frac{d y}{d x} &=n \sin ^{n-1} x \cos x \cos n x-n \sin ^{n} x \sin n x \\
&=n \sin ^{n-1} x[\cos x \cos n x-\sin x \sin n x] \\
&=n \sin ^{n-1} x \cos (n+1) x
\end{aligned}
$$
$$
\begin{aligned}
\frac{d y}{d x} &=n \sin ^{n-1} x \cos x \cos n x-n \sin ^{n} x \sin n x \\
&=n \sin ^{n-1} x[\cos x \cos n x-\sin x \sin n x] \\
&=n \sin ^{n-1} x \cos (n+1) x
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.