A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

If f (x) = 4sin(x)+3(x^x), find f'(2).

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

    Find the derivative of f'(x) and then plug 2 into it.

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

    i have difficulty on finding the f'(x)

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

    The challenge is 3x^x. (1) Set y=3x^x. (2) ln y=xln3x. (3)Solve this as implicit differentiation with the left side giving you derivative of y and chain rule dy/dx. Solve for dy/dx. Move y quantity to right side of eq. Plug in value of y from (1). I am being evasive so you work it out yourself.

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

    y=3x^x lny=xln3x y'/y=1*ln3x+(3/3x)*x y'=(ln3x+1)3x^x is that it?

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

    Good job. I think you got it.

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

    but i still got a wrong answer...

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

    Show us what you got. Some times answers written in different forms meaning the same thing. Master's students write these answer things; they have no sense of humor.

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

    f'(x)=4(cosx)+(ln3x+1)*3x^x f'(2)=4(cos2)+(ln6+1)*12 correct answer was 18.6531788205308

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

    The derivative is going to be f'(x) = 4cos(x) + 3x^x(1+ln(x))...

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

    counld you show me how to get this part (1+ln(x))? coz i got this part wrong and i didnt know how to do this. thanks!

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

    y=3x^x ln(y) = ln(3x^x) * Note where you made a mistake, you can't drop the ^x in front of the log until you take care of the three in front of it, first. ln(y) = ln(3) + ln(x^x) ln(y) = ln(3) x + xln(x) Differentiate... y / y' = ln x + 1 y = 3x^x (lnx + 1)

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

    Sorry, ln(y) = ln(3) x + xln(x)... Should be... ln(y) = ln(3) + xln(x)...

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

    i see! so we need to apply the product rule too when we take the ln?

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

    Yeah, because you have a function of x (just x itself) times another function of x (being ln x)

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

    As far as I can tell you got the calculus right. The number is off two units one way or another. Calculators are very specific and it easy to send wrong info when calculating ln and cos. I think your teacher would give you credit. Then important lesson here is learning how to manipulate the variable when it is in the exponent.

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

    The process was correct, but he needs to make sure he's using the logarithm rules correctly... ln(a*b^x) != x ln(a * b). Need to split it into ln a + ln (b^x) first.

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

    how about differntiating x^x?

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

    i thought its (x^x) (lnx)?

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

    You would get the same thing, except for where you multiple x back in, at the end.. Think about it. All the step did where you split the log from ln (ax^x) into ln a + ln(x^x) was produce a constant which disappears in the differentiation. The only part that would produce something with the a in it, would be where you multiple each side by y, to isolate y' in the last step...

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

    Yeah, a possible mistake. In step (2) try is 3xlnx.

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

    multiply y back in* tired

  22. 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.