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