A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

???

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

    \(f(x) = (x+2)^{7x}\) , right?

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

    Yes

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

    so, \(y= (x+2)^{7x}\) ln both sides, what do you get?

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

    What do you mean?

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

    \(ln\), or log .

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

    I did chain rule and got 7x(x+2)^(6x)

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

    No way!! this is an exponent function with variable on the exponent. You use chain rule if the exponent is a constant. Only one way to take the exponent down is take \(ln\) both sides and use implicit derivative to find dy/dx.

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

    Im not sure how to do that

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

    ok, I do it for you as sample \(ln y = 7x ln(x+2)\) Now take derivative both sides \(\dfrac{y'}{y}= 7ln(x+2) +\dfrac{7x}{x+2}\) multiple y both sides, and replace \(y = (x+2)^{7x}\) , you get the answer

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

    Okay so it would be (7ln(x+2) + 7x/(x+2))(x+2)^7x

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

    yes

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

    Thank you!!

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

    oops used implicit differentiation another way is to use this factoid (by definition): \[ x= e^{\ln x } \] use that to say \[ (x+2)= e^{\ln(x+2)} \] and \[ (x+2)^{7x}= \left(e^{\ln(x+2)} \right)^{7x} \\y= e^{7x\ln(x+2)} \] now you can take the deriviative

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

    Thank you so much @phi !!!

  15. 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.