Question

If `f(x) = (3x^2 + x)/(3x^2 -x)`, what is `f'(x)`?

Answer 1

`f'(x)=-6/(3x-1)^2`

Explanation:

`f^'((3x^2+x)/(3x^2-x))=?`
`f(x)=(cancel(x)(3x+1))/(cancel(x)(3x-1))`
`f^'(x)=(3(3x-1)-3(3x+1))/(3x-1)^2`
`f^'(x)=(3(3x-1-3x-1))/(3x-1)^2`
`f'(x)=-6/(3x-1)^2`