$(fog{)}'(1)={g}'(1)\times {f}'(g(1))$  $g(1)=2$  $\underset{h\to 0}{\mathop{\lim }}\,\frac{f(2+3h)-f(2-h)}{h}=5\xrightarrow{hop}\underset{h\to 0}{\mathop{\lim }}\,3{f}'(2+3h)+{f}'(2-h)=5\Rightarrow 4{f}'(2)=5\Rightarrow {f}'(2)=\frac{5}{4}$  ${g}'(x)=\frac{3}{2\sqrt{3x+1}}\Rightarrow {g}'(1)=\frac{3}{4}\Rightarrow (fog{)}'(1)=\frac{3}{4}\times {f}'(2)=\frac{3}{4}\times \frac{5}{4}=\frac{15}{16}$