amy0799
  • amy0799
if f(x) = 4/(x-2), find f'(x)
Calculus1
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
i am guessing that this is the very beginning of calc and you have to do with by hand, not using any shortcuts am i right?
amy0799
  • amy0799
yup
anonymous
  • anonymous
too bad

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
next week you will say \[f'(x)=-\frac{4}{(x-2)^2}\] in your head, but i guess we can take the steps (long and arduous steps)
anonymous
  • anonymous
we will have to go nice an slow first write the definition, then use some algebra ok a lot of algebra it is 99% algebra
anonymous
  • anonymous
did you get to \[\huge \lim_{h\to 0}\frac{\frac{4}{(x+h-2)}-\frac{4}{x-2}}{h}\]
amy0799
  • amy0799
yes.
anonymous
  • anonymous
ok now in order to spare some agony lets forget about the h in the denominator, and forget about the limit we will deal with those last, ok?
amy0799
  • amy0799
ok
anonymous
  • anonymous
so the algebra we need is to (carefully) do this subraction \[\frac{4}{x+h-2}-\frac{4}{x-2}\]
amy0799
  • amy0799
(4(x-2)-4(x+h-2))/((x-2)(x+h-2) is that right?
anonymous
  • anonymous
can you do this? leave the denominator in factored form i.e don't multiply out
anonymous
  • anonymous
yes that is correct now carefully multiply out in the numerator and combine like terms
amy0799
  • amy0799
(4x-4x-8+8-4h)/((x-2)(x+h-2))
anonymous
  • anonymous
ok that is multiplying out what is left in the numerator?
amy0799
  • amy0799
-4h
anonymous
  • anonymous
exactly!
anonymous
  • anonymous
now recall there is an \(h\) in the denominator cancel it
anonymous
  • anonymous
what is left?
amy0799
  • amy0799
-4/((x-2)(x+h-2))
anonymous
  • anonymous
bingo
anonymous
  • anonymous
now 'take the limit as h goes to zero" which is a fancy way of saying erase that h what is left?
amy0799
  • amy0799
-4/(x-2)^2
anonymous
  • anonymous
as promised (see above)
amy0799
  • amy0799
thank u so much! :D
anonymous
  • anonymous
YW!

Looking for something else?

Not the answer you are looking for? Search for more explanations.