Question

How do you differentiate `g(x)=(3-1/x)/(x+5)` using the quotient rule?

Answer 1

I would change the form first.

Explanation:

Multiply by `x/x` to get

`g(x) = (3x-1)/(x^2+5x)`

So,

`g'(x) = ((3)(x^2+5x)-(3x-1)(2x+5))/(x^2+5x)^2`

`= (3x^2+15x-6x^2-15x+2x+5)/(x^2+5x)^2`

`= (-3x^2+2x+5)/(x^2+5x)^2`