Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

steel11

  • 2 years ago

derivative of 2xsin(1/x) my answer i put, which is wrong 2sinx^-1*cosx^-1*-1x^-2 can anybody give me correct answer or find where i went wrong? im doing the chain rule, and i think you have to do twice, which i did. btw, i brought the x to the numerator with -1 as exponent.

  • This Question is Closed
  1. RadEn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hi uzu :)

  2. uzumakhi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do u know abut product derivation d\dx(a*b) = a d\dx(b) + b d\dx(a)

  3. steel11
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    product rule? yes

  4. uzumakhi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    try to use it

  5. steel11
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I would like to do this with chain rule. If thats possible, which I think it is.

  6. uzumakhi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    try to use my method and tell me the answer u got

  7. across
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Let\[f(x)=2x\sin\left(\frac1x\right).\]Then\[f'(x)=2\sin\left(\frac1x\right)+2x\cos\left(\frac1x\right)\cdot\left(-\frac1{x^2}\right)=2\left[\sin\left(\frac1x\right)-\frac1x\cos\left(\frac1x\right)\right].\]

  8. steel11
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you across. you used product rule and chain rule to solve right?

  9. steel11
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    guess uzumaki was right on having to use product rule. ._.

  10. uzumakhi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that what i am talking about thanx @across

  11. steel11
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    =]

  12. across
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes. To be more specific, let me break it down for you: Essentially, you have this:\[f(x)=g(x)h(j(x)),\]where\[g(x)=2x\\h(x)=\sin x\\j(x)=\frac1x.\]Then\[f'(x)=g'(x)h(j(x))+g(x)h'(j(x))j'(x),\]and since\[g'(x)=2\\h'(x)=\cos x\\j'(x)=-\frac1{x^2},\]we have that\[f'(x)=2\cos\left(\frac1x\right)+2x\cos\left(\frac1x\right)\cdot\left(\frac1{x^2}\right).\]

  13. across
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I forgot the negative sign in the last term, but you get the idea. I used the product and chain rules.

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.