Question

Is it possible to find the derivative of `3x/(x^2+4)` without using the quotient rule?

Answer 1

Actually yes...if you write it as:
`y=3x(x^2+4)^-1` so that you could use the Product and Chain Rule:
`y'=3(x^2+4)^-1-3x(x^2+4)^-2(2x)=`
`=3(x^2+4)^-1[1-2x^2(x^2+4)^-1]=`
`=3/(x^2+4)[1-2x^2/(x^2+4)]=`
`=3/(x^2+4)^2[x^2+4-2x^2]=`
`=3/(x^2+4)^2[4-x^2]`