To find the root of the equation $f(x) \equiv e^{-x} - x = 0$, the Newton-Raphson method is used. If the initial guess for the root is 1, then the estimate of the root after first iteration is _______}
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Be careful with the signs during the derivative and division steps.
The negative derivative term $-e^{-x} - 1$ cancels the subtraction sign in the Newton-Raphson formula, converting the operation into simple addition.