To find the derivative of the function we will use Chain Rule: (d)/(dx)[f(g(x))=f'(g(x))=g'(x)] h'(x)=f'(g(x))g'(x) Plug in x=1 to find h'(1). h'(1)=f'(g(1))g'(1) =f'(4)g'(1) =(-1)*(-(1)/(2)) =(1)/(2) To estimate f'(4), there is a part of the picture where we can see that the tangent line goes down 1 unit as the variable x moves one unit to the . This means that it has slope -1, thus f'(4)=-1. To estimate g'(1), there is a part of the picture where we can see that the tangent line goes down 1 unit as the variable x moves two units to the . This means that it has slope -(1)/(2), thus g'(1)=-(1)/(2). Result: a=(1)/(2)