Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

cunninnc

  • 3 years ago

find the derivative of y=log10(5x^4-2/x^3)

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

    this involves both the chain rule and the quotient rule

  2. Mimi_x3
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    or you can use log laws to change it first; then diferentiate it, would be easier.

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

    @failmathmajor only the 2/x^3 is a fraction

  4. Mimi_x3
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is it \[\log\left(5x^{4}-\frac{2}{x^{3}}\right) ?\]

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

    that would be much easier

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

    so using log properties you can say that \[\log_{10} {x} = \ln x / \ln 10 \]

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

    ln10 is a constant, you can factor that out

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

    can you use the chain rule fluently?

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

    y'=pu(x) * u'(x) right?

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

    d(f(g(x))/dx = (dg(x)/dx)*(df(g(x))/dx) is the way I know it

  11. Mimi_x3
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Or..\[y= \log\left(5x^{4}-\frac{2}{x^{3}}\right) y = \log\left(\frac{5x^{7}-2}{x^{3}}\right) => y = \log\left(5x^{7}-2\right) - \log(x^3)\] Might be easier; than the quotient role and chain rule..

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

    that may look confusing now that I see it

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

    don't need the quotient in this case: can treat /x^3 as a x^-3

  14. Mimi_x3
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @cunninnc: are you able to do it now?

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

    and you would still need the chain rule for that anyway

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

    but enough arguing

  17. Mimi_x3
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Did an argument started? lol

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

    \[(d(\ln (5x^4 - 2x^{-3}))/dx )/ \ln10\] is what it simplifies down to, to be concise

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

    @Mimi_x3 kinda .... i see mr. moose got 2x^-3 where does ^-3 come froms

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

    \[2/x^3= 2 * x^{-3}\]

  21. Mimi_x3
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry i don't know what MrMoose is doing. @MrMoose: Use \frac{x}{y} for fractions :)

  22. Mimi_x3
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Or why not try the method that i used :) \[ \frac{d}{dx} \log\left(5x^{7}-2\right) -\frac{d}{dx} \log(x^3)\]

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

    when you divide you subtract exponents, so that is equivalent to saying \[2 * \frac{x^0}{x^3}\] then subtract exponents in division

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

    \[\frac{\frac{d(\ln(5x^4−2x^{−3}))}{dx}}{\ln10}\]

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

    @catamountz15 what?

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

    I am almost entirely sure that that isn't a form of the answer.

  27. catamountz15
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Here are the steps in to solving this problem.

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

    that isn't what you wrote though

  29. catamountz15
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    My apologies that was an answer to a different problem.

  30. 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.