what is f'(0) if f(x)=e^x -x ?

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You need first to evaluate derivative of the function, such that:

`f'(x) = (e^x - x)' => f'(x) = (e^x)' - (x)'`

`f'(x) = e^x - 1`

You need to evaluate the derivative of the function at `x = 0` , hence, you should replace 0 for x in equation of derivative, such that:

`f'(0) = e^0 - 1 => f'(0) = 1 - 1 => f'(0) = 0`

Hence, evaluating the derivative of the given function, at x = 0, yields `f'(0) = 0.`

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