Final answer:
The derivative of the function f(x) = e⁻²ˣ - x evaluated at x = 2 is found by applying the chain rule and the result is f'(2) = -2e⁻⁴ - 1.
Step-by-step explanation:
To evaluate the derivative at x = 2 for the function f(x) = e⁻²ˣ - x, we first need to find the derivative of the function. The derivative of e⁻²ˣ with respect to x is -2e⁻²ˣ, since the chain rule must be applied to the exponent -2x, which is itself a function of x. The derivative of -x is simply -1. Combining these results, the derivative of the function f(x) is f'(x) = -2e⁻²ˣ - 1.
Evaluating this derivative at x = 2 gives us f'(2) = -2e⁻⁴ - 1. Therefore, the derivative at x = 2 is the value of this expression.