Question

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

Answer 1

`h'(x) = (color(red)(6x)color(green)((3x+1)) - color(blue)(3)(3x^2-4))/(color(green)((3x+1)^2)`

Explanation:

Given:
`Let h(x) = f(x)/g(h)`
Quotient Rule says:
`h'(x) = (g(x)f'(x) - g'(x)f(x))/[g(x)]^2`
Now in your case set:
1) `f(x) = 3x^2-4; " then " f'(x) = color(red)(6x)`
2) `g(x) = color(green)(3x+1); " and " g'(x) = color(blue)3`

Solution is:
`h'(x) = (color(red)(6x)color(green)((3x+1)) - color(blue)(3)(3x^2-4))/(color(green)((3x+1)^2)`

Note I used: `h'(x) = (dh(x))/(dx)`
Cheers!