calculus - How to differentiate $F(y) = left(frac{1}{y^2}-(frac{-2}{y^4})right)cdotleft(y+5y^{3}right)$

I tried to differentiate this function, and was able to differentiate the second portion $(y + 5y^3)$, but I could not differentiate the $\left(\frac{1}{y^2}-(\frac{-2}{y^4})\right)$ term. Now I know that to complete the differentiation I need to multiply the first term by $(15x^2+1)$, but how do I get the term to multiply by $(y+5y^3)$ and simplify?

Answer

Write the term $\frac{1}{y^2}$ as $y^{-2}$ so

$$(\frac{1}{y^2})'=(y^{-2})'=-2\times y^{-2-1}=-2\times y^{-3}$$ Now, do the same to $\frac{1}{y^4}$. Note that, I assumed $y$ is an independent variable here.