Question

How do you differentiate `f(x)= (3x^2+4x+2)/ (3x +1 )` using the quotient rule?

Answer 1

`f'(x)=(9x^2+6x-2)/(3x+1)^2`

Explanation:

differentiate using the `color(blue)"quotient rule"`

Given `f(x)=(g(x))/(h(x))" then "`

`color(red)(|bar(ul(color(white)(a/a)color(black)(f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2))color(white)(a/a)|))........ (A)`
`color(blue)"--------------------------------------------------------"`

`g(x)=3x^2+4x+2rArrg'(x)=6x+4`

`h(x)=3x+1rArrh'(x)=3`
`color(blue)"------------------------------------------------------"`
substitute these values back into (A)

`f'(x)=((3x+1)(6x+4)-(3x^2+4x+2).3)/(3x+1)^2`

`=(18x^2+18x+4-9x^2-12x-6)/(3x+1)^2`

`rArrf'(x)=(9x^2+6x-2)/(3x+1)^2`