Calculus of a Single Variable, Chapter 5, 5.8, Section 5.8, Problem 24

f(x)=cosh(8x+ 1)
Take note that the derivative formula of cosh is
d/dx[cosh(u)] = sinh(u) *(du)/dx
Applying this formula, the derivative of the function will be
f'(x) = d/dx [cosh(8x+1)]
f'(x) = sinh(8x + 1)*d/dx(8x+1)
f'(x)=sinh(8x + 1) * 8
f'(x) = 8sinh(8x +1)

Therefore, the derivative of the function is f'(x) =8sinh(8x+1) .