$(20$ Points$)$ Consider the graphs of functions $f($on the left$)$ and $g.$ Each drawn below with their tangent line drawn at $(0,1).$

Find $\frac{d}{dx}g(x)\sqrt[\phantom{2}]{f(x)}$ evaluated at $x=0.$

Find $\frac{d}{dx}sin(\frac{f(x)}{g(x)})$ evaluated at $x=0.$

Find $\frac{d}{dx}{e}^{f(x)g(x)}$ evaluated at $x=0.$

Find evaluated at $x=0.$