$\displaystyle F(y)=(\frac{1}{y^2}-\frac{3}{y^4})(y+5y^3)$

I'm not sure where to start so I tried to get rid of the fraction.

$\displaystyle

(y^4)(\frac{1}{y^2}-\frac{3}{y^4})(y+5y^3)$

$\displaystyle =(y^2-3)(y^5+5y^7)$

now I differentiated

$\displaystyle (2y-0)(y^5+5y^7)+(y^2-3)(5y^4+35y^6)$

which turns into a ridiculously large.. and wrong answer after i simplify $\displaystyle

45y^8-38y^6-15y^4$

book's answer is $\displaystyle

5+\frac{14}{y^2}+\frac{9}{y^4}$