Question

How do you differentiate this problem?

Answer 1

`(dy)/(dx)` =
`(5)/((x+2)^2)`

Explanation:

Differentiate using the quotient rule.

Given y =
`(f(x))/(g(x))` , then

`(dy)/(dx)` =
`(g(x)f'(x)-f(x)g'(x))/((g(x))^2)`

here f(x) = 3x + 1 ⇒ f'(x) = 3

g(x) = x + 2 ⇒ g'(x) = 1 , thus

`(dy)/(dx)` =
`(3(x+2)-(3x+1))/((x+2)^2)`

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

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