1. The problem states: Given the function $f(x) = \sec^2 x - \tan^2 x$, find the derivative evaluated at $x = -1$, i.e., calculate $f'(-1)$.\n\n2. Recall the trigonometric identity: $$\sec^2 x - \tan^2 x = 1.$$\nThis means $f(x) = 1$ for all values of $x$.\n\n3. Since $f(x)$ is a constant function, its derivative is zero everywhere: $$f'(x) = 0.$$\n\n4. Therefore, evaluating the derivative at $x = -1$ gives: $$f'(-1) = 0.$$\n\n5. The correct answer choice is (b) zero.