anonymous
  • anonymous
Find the derivative of f(x) = 1/ x+9 by using the difference quotient.
Mathematics
  • 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
(x+9)^2?
anonymous
  • anonymous
\[-h / (x+h+9)(x+9)\]
anonymous
  • anonymous
am I right or can I go further

Looking for something else?

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

More answers

DebbieG
  • DebbieG
I think you're missing factor of h....? That h in the num'r should cancel with h in the den'r of the original DQ.
DebbieG
  • DebbieG
\[ \dfrac{ \dfrac{ 1 }{ x+h+9 } - \dfrac{ 1 }{ x+9 }}{ h }\] \(= \dfrac{ \dfrac{ x+9-(x+h+9) }{ (x+h+9)(x+9) } }{ h }\) \(= \dfrac{ -h }{ (x+h+9)(x+9) } \cdot \dfrac{1}{ h }\)
DebbieG
  • DebbieG
So the -h and the h cancel, leaving a -1 in the num'r..... then take the limit.
anonymous
  • anonymous
wow I forgot it pretty much
DebbieG
  • DebbieG
@asdafogbucket I'm not sure how you got that... that isn't the correct DQ for this problem. I thought at first that you did the DQ for f(x) = 1/ x+9, which IS what was written (he meant f(x) = 1/ (x+9), it seems)... but yours wouldn't be correct for f(x) = 1/ x+9, either.
anonymous
  • anonymous
so m'(x) = \[-1 / (x+9)^2\]
DebbieG
  • DebbieG
Is the function was, in fact, f(x)=(1/x) + 9, then the DQ would be: \[\Large \dfrac{ \dfrac{ 1 }{ x+h } + 9 - (\dfrac{ 1 }{ x } + 9)}{ h }\] the "x+h" must be together in that num'r, and the parentheses around the "-f(x)" part are what I like to call, "NON-optional parentheses!" :)
DebbieG
  • DebbieG
Yes, exactly @smallmelo - that's it! :)
anonymous
  • anonymous
thanks!
DebbieG
  • DebbieG
no problem,happy to help. :)

Looking for something else?

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