find dxy

y=6x-8/(x-8)

u= 6x-8 v=x-8
u' = 6 v'=1

(6x-8)1 + (x-8)6 /(x-8)^2

and I get -56 / (x-8)^2 but the answer should be -40 / (x-8)^2 . So what did I do wrong?

Question

find dxy

y=6x-8/(x-8)

u= 6x-8    v=x-8
u' = 6        v'=1

(6x-8)1 + (x-8)6 /(x-8)^2

and I get -56 / (x-8)^2 but the answer should be -40 / (x-8)^2 . So what did I do wrong?

phi · Answer

isn't the rule
$$ \frac{d}{dx}\frac{u}{v} = \frac{v\ du - u\ dv}{v^2} $$

phi · Answer

you are adding , not subtracting

anonymous · Answer

oh right... but when I do that I get 40 instead of -40 for the numerator.

phi · Answer

yes, it is v du - u dv
(v is the denominator and u is the numerator)

anonymous · Answer

Okay. SO i just got the formula backwards.

phi · Answer

yes, I can never remember it.

phi · Answer

if I get confused I write it as
(6x-8) (x-8)^-1
and use the product rule.   I think the other way is faster, but you have to remember what gets subtracted.

anonymous · Answer

True. Thanks for the help!