So, after being given the following prompt:
"The table above gives selected values for a differentiable and decreasing function $g$ and its derivative. Let $f$ be the function with $f(3) = 2$ and derivative given by $f'(x)=x \cos(e^x)$"
I was given the question that went something like this: "Let $h$ be the function defined by $h=g(f(2x)).$ Find $h'(1.5).$" I figured that I should use chain rule in the first steps of this problem, which after the application of it led me to the equation of $g'(f(2x)) * 2f'(x)$ (which I have absolutely no clue if this is correct), but I'm a bit stuck on actually plugging the $1.5$ value into $f(x)$. I know that I have to find the original equation for $f(x)$ in order to plug this value in, but I've been working at the integral of $f'(x)$ for some time now and I can't seem to find that either. Any help would be appreciated!
$$h'(x)\big|_{x=1.5}=g'(f(2x)) \cdot 2f'(2x)\big|_{x=1.5}=g'(f(3))2f'(3)=2\cdot g'(2)\cdot f'(3)=\\ =2\cdot (-3)\cdot 3\cos(e^3)$$