$\begin{array}{l}f(x)=\left(x^{4}-2 x\right) \\ g(x)=\left(x^{2}+8 x-83\right) \\ h(x)=2 x-11 \\ m(x)=f(x) \cdot g(x) \\ h(x)=\frac{g(x)}{h(x)} \\ m^{\prime}(-1)=\end{array}$

Step 1 ：Given the functions \(f(x) = x^{4} - 2x\), \(g(x) = x^{2} + 8x - 83\), \(h(x) = 2x - 11\), and \(m(x) = f(x) \cdot g(x)\), we are asked to find the derivative of \(m(x)\) at \(x = -1\).

Step 2 ：We can use the product rule to find the derivative of \(m(x)\). The product rule states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.

Step 3 ：First, we find the derivatives of \(f(x)\) and \(g(x)\). The derivative of \(f(x)\) is \(f'(x) = 4x^{3} - 2\), and the derivative of \(g(x)\) is \(g'(x) = 2x + 8\).

Step 4 ：Then, we apply the product rule to find the derivative of \(m(x)\): \(m'(x) = f'(x)g(x) + f(x)g'(x) = (4x^{3} - 2)(x^{2} + 8x - 83) + (x^{4} - 2x)(2x + 8)\).

Step 5 ：Finally, we substitute \(x = -1\) into \(m'(x)\) to find the value of the derivative at that point: \(m'(-1) = 558\).

Step 6 ：Final Answer: The derivative of the function \(m(x)\) at \(x = -1\) is \(\boxed{558}\).