Im getting the wrong answer to this simple derivative problem

find the derivative of
y = 1/x + 4x

simple enough. i found the derivative to be
1/x² + 4
but the back of the book gives the answer to be
(x^ -2) (2x-1)(2x+1)
i understand the x^-2 its just pulled up from the denominator but where did they get the rest of the expression. or is the book answer wrong?

(x^ -2) (2x-1)(2x+1) =
(2x-1)(2x+1) / x^2 =
(4x^2 - 1) / x^2 =
4 - 1/x^2

The book has the right answer. I'm guessing they combined the fractions then used the quotient rule. Then factored the numerator. This is a silly way to do it though.

You are missing a negative in your answer.
1/x = x^(-1)
Using the power rule gives you the derivative -x^(-2)

book ok ur wrong

deriv = -1/x^2 +4 note the - sign

rest is easy