A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

I have a calculus problem: cubed root of (x^3+6x+1) times x^7 I have worked out part of this problem but there is a part which I will identify that I am unsure of how the solution is arrived at. Let F(x)=f(x)*g(x) Let f(x)= (x³+6x+1)^(1/3) d/dx (x³+6x+1)^(1/3)= (x²+2)/(x³+6x+1)^(2/3) Let g(x)=x^7 d/dx x^7= 7x^6 F'(x)= (x³+6x+1)^(1/3)*7x^6 +x^7 * (x²+2)/(x³+6x+1)^(2/3) read next

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

    Now here is where I am having problems . . . The next step in the solution shows the f(x) as [(x³+6x+x)^(1/3) * 7x^6]/(x³+6x+1)^(2/3) + a second portion which I will leave off for the time being. My question is how [(x³+6x+x)^(1/3) got in the numerator and what happened to the 3 that should be in the denominator?

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

    Are you wanting to simplify f'(x)?

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

    I am trying to figure out what happened with f(x). When I brought the 1/3 in front what happened to to 3 that should be in the denominator? and when I took the (x^3+6x+1)^(-2/3) down to the denominator why did (X^3+6x+1) remain in the numerator?

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

    they applied the chain rule, then factored, so the 3 in the denominator canceled.

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

    oh, I think I figured it out f(x)*d/dx g(x) + g(x) * d/dx f(x) is all over d^2 right

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

    |dw:1442968002532:dw|

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

    no, for product rule, it's not over d^2

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

    ok, got it. Thanks

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

    (fg)' = f ' g + g' f

  10. 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.