Answer
$f^{\prime}(x)=8\sinh(8x+1)$
Work Step by Step
Apply Th. 5.18:
Let $u$ be a differentiable function of $x$.
$ \displaystyle \frac{d}{dx}[\cosh u]=(\sinh u)u^{\prime}$
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$ \displaystyle \frac{d}{dx}[\cosh(8x+1)]=(\sinh(8x+1))(8x+1)^{\prime}=(\sinh(8x+1))\cdot 8$
$f^{\prime}(x)=8\sinh(8x+1)$
