Answer:
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{5}{(x+2)^2}[/tex]
Step-by-step explanation:
Differentiate using the quotient rule.
Given y = [tex]\frac{f(x)}{g(x)}[/tex] , then
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}[/tex]
here f(x) = 3x + 1 ⇒ f'(x) = 3
g(x) = x + 2 ⇒ g'(x) = 1 , thus
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{3(x+2)-(3x+1)}{(x+2)^2}[/tex]
= [tex]\frac{3x+6-3x-1}{(x+2)^2}[/tex]
= [tex]\frac{5}{(x+2)^2}[/tex]
