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 / derivative problem that I am unable to understand how the last step is worked out. The problem is y=(2x-5)^3(1-x^4)^2 working it out I get: (2x-5)^3 [2(1-x^4)(-4x^3)] + (1-x^4)^2 [3(2x-5)^2 (2)] which is (2x-5)^3[-8x^3(1-x^4)] +(1-x^4)^2[6(2x-5)^2] The online guide says to now factor and ends up with 2(2x-5)^2(1-x^4)[-11x^4+20x^3+3] I am unable to see what was factored and how the final answer was arrived at. Any help is appreciated. Straight answers are best. Asking me to try and guess is frustrating to me. Thanks

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

    \[y=(2x-5)^3(1-x^4)^2\]And you're trying to take the derivative of this using the product rule - \(f'g + g'f\)?

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

    yes

  3. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you did: \[y=(2x-5)^3(1-x^4)^2\] \[(2x-5)^3 [2(1-x^4)(-4x^3)] + (1-x^4)^2 [3(2x-5)^2 (2)]\] \[(2x-5)^3[-8x^3(1-x^4)] +(1-x^4)^2[6(2x-5)^2]\] and they want \[2(2x-5)^2(1-x^4)[-11x^4+20x^3+3]\] right?

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

    yes

  5. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    make it easy for yourself write (2x-5) as A and (1-x^4) as B then try

  6. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you have \[A^3[-8x^3B] +B^2[6A^2] \] they want \[2A^2B[-11x^4+20x^3+3]\] something's gotta give!!

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

    I don't understand. I cannot see the relation

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

    \(\large\color{black}{ \displaystyle y=(2x-5)^3(1-x^4)^2 }\) \(\large\color{black}{ \displaystyle\ln y= \ln\left[(2x-5)^3(1-x^4)^2\right] }\) \(\large\color{black}{ \displaystyle \ln y=\ln\left[(2x-5)^3\right]+\ln\left[(1-x^4)^2\right] }\) \(\large\color{black}{ \displaystyle \ln y=3\ln\left[2x-5\right]+2\ln\left[1-x^4\right] }\) \(\large\color{black}{ \displaystyle \frac{y'}{y}=3\cdot \frac{2}{2x-5}+2\cdot\frac{4x^3}{1-x^4} }\) \(\large\color{black}{ \displaystyle y'=y\left(\frac{6}{2x-5}+\frac{8x^3}{1-x^4}\right) }\) \(\large\color{black}{ \displaystyle y'=(2x-5)^3(1-x^4)^2\left(\frac{6}{2x-5}+\frac{8x^3}{1-x^4}\right) }\)

  9. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[y=(2x-5)^3(1-x^4)^2\]\[y' = 3\color{blue}{(2x-5)^2}(2)\cdot \color{red}{ (1-x^4)^2} +2\color{red}{(1-x^4)}(4x^3)\cdot \color{blue}{(2x-5)^3}\]\[y'= \color{blue}{(2x-5)^2}\color{red}{(1-x^4)}\left[6(1-x^4)+2(4x^3)(2x-5)^2\right]\]\[y'=\color{blue}{(2x-5)^2}\color{red}{(1-x^4)}\left[6-6x^4+8x^3(4x^2-20x+25)\right]\]\[y'=\color{blue}{(2x-5)^2}\color{red}{(1-x^4)}\left[6-6x^4+32x^5-160^4+200x^3\right]\]\[\boxed{y'=\color{blue}{(2x-5)^2}\color{red}{(1-x^4)}\left[6-166x^4+32x^5+200x^3\right]}\] @SolomonZelman check my work lol

  10. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think I forgot a negative somewhere in there.

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

    -4x^3 is a negative chain

  12. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yep. I spotted it too

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

    oh, I left it out too.

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

    \(\large\color{black}{ \displaystyle y=(2x-5)^3(1-x^4)^2 }\) \(\large\color{black}{ \displaystyle\ln y= \ln\left[(2x-5)^3(1-x^4)^2\right] }\) \(\large\color{black}{ \displaystyle \ln y=\ln\left[(2x-5)^3\right]+\ln\left[(1-x^4)^2\right] }\) \(\large\color{black}{ \displaystyle \ln y=3\ln\left[2x-5\right]+2\ln\left[1-x^4\right] }\) < ☼ CORRECTION ☼ > \(\large\color{black}{ \displaystyle \frac{y'}{y}=3\cdot \frac{2}{2x-5}+2\cdot\frac{-4x^3}{1-x^4} }\) \(\large\color{black}{ \displaystyle y'=y\left(\frac{6}{2x-5}-\frac{8x^3}{1-x^4}\right) }\) \(\large\color{black}{ \displaystyle y'=(2x-5)^3(1-x^4)^2\left(\frac{6}{2x-5}-\frac{8x^3}{1-x^4}\right) }\)

  15. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[y' = 3\color{blue}{(2x-5)^2}(2)\cdot \color{red}{ (1-x^4)^2} +2\color{red}{(1-x^4)}(4x^3)\cdot \color{blue}{(2x-5)^3}\]\[y'= \color{blue}{(2x-5)^2}\color{red}{(1-x^4)}\left[6(1-x^4)+2(-4x^3)(2x-5)^2\right]\]\[y'=\color{blue}{(2x-5)^2}\color{red}{(1-x^4)}\left[6-6x^4-8x^3(4x^2-20x+25)\right]\]\[y'=\color{blue}{(2x-5)^2}\color{red}{(1-x^4)}\left[6-6x^4-32x^5+160^4-200x^3\right]\]\[\boxed{y'=\color{blue}{(2x-5)^2}\color{red}{(1-x^4)}\left[6-154x^4-32x^5-200x^3\right]}\] Theres my correction.

  16. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\boxed{y'=\color{blue}{(2x-5)^2}\color{red}{(1-x^4)}\left[6+154x^4-32x^5-200x^3\right]}\]

  17. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @mthompson440 i meant this by the suggestion: write (2x-5) as A and (1-x^4) as B with the simplifications, they want \[2A^2B[-11x^4+20x^3+3]\] you have \(A^3(-8x^3B) +B^2[6A^2]\) \(= 2A^3B(-4x^3) + 3A^2 B^2\) \(= 2A^2B(A(-8x^3) + 6B)\) \(= 2A^2B(-4(2x-5)x^3+3(1-x^4))\) \(= 2A^2B(-8x^4+20x^3+3-3x^4))\) \(= 2A^2B(-11x^4+20x^3+3))\) there's no silver bullet for this kind of mess. just look up at this thread! that was just a suggestion as to how to make life easier. i am sure you can think of your own :p

  18. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Where is the koala bear?

  19. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Jhannybean \[y'= \color{blue}{(2x-5)^2}\color{red}{(1-x^4)}\left[6(1-x^4)+2(-4x^3)(2x-5)^\color{green}{1}\right]\]

  20. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I put the correction in green because you already used the prettier colors

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

    Refer to the attachment from Mathematica v9.

    1 Attachment
  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.