anonymous 5 years ago if for all x>0, G(x)= $\int\limits_{1}^{x}\sin (\ln 2t)dt$ , then the value of G''(1/2) is?

1. anonymous

first derivative is $\sin(\ln(2x))$

2. anonymous

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

3. anonymous

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