Let's go ;D
[tex]f(y)=\frac{y^2}{y^3+8}[/tex]
we have to use the quotient rule.
[tex]f(y)=\frac{g(y)}{h(y)}[/tex]
[tex]f'(y)=\frac{h(y)*g'(y)-g(y)*h'(y)}{[h(y)]^2}[/tex]
Then
[tex]g(y)=y^2[/tex]
[tex]g'(y)=2y[/tex]
[tex]h(y)=y^3+8[/tex]
[tex]h(y)=3y^2[/tex]
Now we can replace
[tex]f'(y)=\frac{h(y)*g'(y)-g(y)*h'(y)}{[h(y)]^2}[/tex]
[tex]f'(y)=\frac{(y^3+8)*2y-(y^2)*3y^2}{(y^3+8)^2}[/tex]
[tex]f'(y)=\frac{2y^4+16y-3y^4}{(y^3+8)^2}[/tex]
[tex]\boxed{\boxed{f'(y)=\frac{16y-y^4}{(y^3+8)^2}}}[/tex]
