Math: Derivatives

Use the shortcut rules to mentally calculate the derivative of the given function
f(x) = −x + (3/x) + 1

After deriving it, I got
-1+(0/1)+0= -1
But this answer is wrong, and I don't know why.
Thank You

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  1. The derivative of f(x) is
    -1-3/x²

    Don't know how you got -1, or what the question really is.

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  2. How did you get the answer? I don't quite understand. Thanks

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  3. If f(x)=g(x)+h(x), then
    linearity gives
    f'(x)=g'(x)+h'(x)
    so
    f(x)=-x + (3/x) + 1
    f'(x)= (-x)' + (3/x)' + (1)'
    =-1 -3/x² + 0
    =-1 -3/x²
    The second term is obtained by the power rule:
    d(1/x)/dx = -1/x²

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