Chapter 3.2, Problem 60E

To determine

To calculate: $\frac{d}{dx}g(f(x)){|}_{x=1}$, where $f(x)$ and $g(x)$ are differentiable functions such that $f(1)=2,f\text{'}(1)=3,f\text{'}(5)=4,g(1)=5,g\text{'}(1)=6,g\text{'}(2)=7$ and $g\text{'}(5)=8$.