Question

The first derivative of the function

($\sin 2x\cos 2x\cos 3x + \log_{2}2^{x + 3})$ with respect to x at $x = \pi$ is

• A. 2
• B. –1
• C. $- 2 + 2^{\pi}\log_{e}2$
• D. $- 2 + \log_{e}2$

Answer 1

Answer: (B)

–1

Answer 2

$f(x) = \sin 2x.\cos 2x.\cos 3x + \log_{2}2^{x + 3}$, $f(x) = \frac{1}{2}\sin 4x\cos 3x + (x + 3)\log_{2}2$, $f(x) = \frac{1}{4}\lbrack\sin 7x + \sin x\rbrack + x + 3$Differentiate w.r.t. x,

$f^{'}(x) = \frac{1}{4}\lbrack 7\cos 7x + \cos x\rbrack + 1$,

$f^{'}(x) = \frac{1}{4}7\cos 7x + \frac{1}{4}\cos x + 1$, $f^{'}(\pi) = - 2 + 1 = - 1$.