Question

if for all x>0, G(x)= \[\int\limits_{1}^{x}\sin (\ln 2t)dt\] , then the value of G''(1/2) is?

Answer 1

first derivative is \[\sin(\ln(2x))\]

Answer 2

second derivative is \[cos(\ln(2x))\times \frac{1}{x}\]

Answer 3

plug in \[\frac{1}{2}\]
get \[cos(\ln(1))\times 2=cos(0)\times 2 = 1\times2 = 2\]