Question

Simple question 

Derivative of 
`\boxed{f(y)= (y^2)/(y^3+8) }`

Answer 1

Let's go ;D


`f(y)=(y^2)/(y^3+8)`

we have to use the quotient rule.


`f(y)=(g(y))/(h(y))`


`f'(y)=(h(y)*g'(y)-g(y)*h'(y))/([h(y)]^2)`

Then


`g(y)=y^2`


`g'(y)=2y`


`h(y)=y^3+8`


`h(y)=3y^2`

Now we can replace


`f'(y)=(h(y)*g'(y)-g(y)*h'(y))/([h(y)]^2)`


`f'(y)=((y^3+8)*2y-(y^2)*3y^2)/((y^3+8)^2)`


`f'(y)=(2y^4+16y-3y^4)/((y^3+8)^2)`


`\boxed{\boxed{f'(y)=(16y-y^4)/((y^3+8)^2)}}`