Question

Let $f\left(x\right)=\tan 2x.\tan 3x.\tan 5x$ , then $f^{{}^{\prime }}\left(\pi \right)$ equals

• A. $10$
• B. $-10$
• C. $0$
• D. $1$

Answer 1

Answer: (C)

$0$

Given, $f\left(x\right)=\tan 2x\tan 3x\tan 5x$

$f\left(x\right)=\tan 5x-\tan 2x-\tan 3x$
$f\left(x\right)=\tan 5x-\tan 2x-\tan 3x$
$f^{{}^{\prime }}\left(x\right)=5{\sec }^{2}5x-2{\sec }^{2}2x-3{\sec }^{2}3x$
$f^{{}^{\prime }}\left(\pi \right)=5-2-3$
$=0$