The first derivative of the function sin 2x cos 2x cos 3x + log₂ 2^x+3 with respect to x at x = π is

(1) 2

(2) -1

(3) 1

(4) none of these

Solution:

Given f(x) = sin 2x cos 2x cos 3x + log₂ 2^x+3

= (½) sin 4x cos 3x + (x+3) log₂ 2

= (½) sin 4x cos 3x + (x+3)

Differentiate w.r.t.x

f’(x) = (½)[ 4cos 4x cos 3x – 3 sin 3x sin 4x ] + 1

f’(π) = ½ [ -4 – 0] + 1

= -2 + 1

= -1

Hence option (2) is the answer.