Question

Im trying to find the derivative of x/(x+2).

I keep getting the answer f'(x)= -x(x+2)^-2 or -x/(x+2)^2. But these are wrong. Can someone please help me.

Answer 1

You COULD use the quotient rule, but I hate that as it's just a special case of the product rule.
Apply the product rule:\[\frac{d(\frac{x}{x+2})}{dx}=\frac{d(\frac{1}{x+2})}{dx}x+\frac{d(x)}{dx}\frac{1}{x+2}\]