A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Find thw anti-derivative of \[f(x)=\frac{ -1 }{ x^2 }e ^{1/x}\]

  • This Question is Closed
  1. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 6

    \[\large -\int \frac{e^{1/x}}{x^2}\] Make a u-sub of 1/x

  2. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 6

    Oh...what have you learned?

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    How do you write in this format? f(x)=F(x)+C

  4. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\Large\rm \int\limits f(x)dx=F(x)+C\]Where F(x) is the anti-derivative of f(x). Did you understand the u-substitution?

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is there another way to solve it without using the u-substitution?

  6. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i can't think of a better way

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The reason that I ask that was because the question was at the beginning of antiderivatives/integration. I learned the u-substitution as a last topic...

  8. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you may use advanced guessing what is the derivative of \(\large e^{1/x}\) ?

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    e^1/x

  10. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what do you know about chain rule

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Chain rule applies to composite function. It describe of outer evulated at inner, times derivative of inner

  12. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 6

    So using that logic...if we consider the "inner" as 1/x The derivative of \(\large e^{1/x}\) would be \(\large \frac{d(1/x)}{dx} \times e^{1/x}\) So what is the derivative of \(\large 1/x\) ?

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lnx?

  14. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you found the antiderivative for positive x

  15. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that you found the antiderivative of 1/x for positive x the question was to differentiate

  16. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    derivative if lnx is 1/x derivative of 1/x is not lnx

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ooh... derivative of 1/x is -1/x^2 ...

  18. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 6

    Correct...and to finish up from the previous post \[\large \frac{d}{dx}e^{1/x} = e^{1/x} \times \frac{d}{dx}\frac{1}{x}\] Since we just found the later \(\large \frac{d}{dx} \frac{1}{x} = -\frac{1}{x^2}\) we have \[\large \frac{d}{dx}e^{1/x} = -\frac{e^{1/x}}{x^2}\] right? Now what do you notice?

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So F(x)= e^{1/x} +C ?

  20. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 6

    Perfect! :)

  21. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you! :) I got it now. I was messed up b/w derivatives and anti-derivatives. My bad...

  22. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 6

    Yeah sometimes they can be hard to keep straight...but as long as you can derive them you're all set!

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.