Sunday, March 8, 2009

Are these solutions correct?

Solution 1

y = log base 3 (8x^7 + x)
u = 8 x^7 + x
dy/dx = 56 x^6 + 1
= (56 x^6 + 1) / (8 x^7 + x) log base 3 e

Solution 2
P = ln 6s^3 + s
u = 6s^3
dy/dx = 18 s^2
= (18s^2)/(6s^3) + 1

Solution 2
P = ln 6s^3 + s
u = 6s^3 + s
dy/dx = 18 s^2 + 1
= (18s^2 + 1)/(6s^3 + s)

Solution 3
y = 15 x^3 + 7/(2x^3) - x
y = 15x3 + 7 *2 x^-3 - x
dy/dx = 45 x^2 + 42 x^-4 - 1

Solution 3
y = 15 x^3 + 7/(2x^3) - x
dy/dx = 45 x^2 + 7/6 x^-2 - 1
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13 comments:

  1. AdriaMarch 9, 2009 at 9:46 AM

    to get dy/dx
    =dy/du*du/dx
    so du's would cancel
    and dy/dx will remain

    ReplyDelete
  2. ghetto_celebMarch 11, 2009 at 5:40 PM

    solution 3 is incorrect.first of all you will recognize that you have upstairs and downstairs in the equation.

    you will make the downstairs 7 / 2 x^3 into upstairs making it (7/2)* x^-3.

    hence rewrite the equation as:
    y = 15 x^3 + (7/2)*x^-3 + x

    differentiating:
    dy/dx =[(15*3)x^(3-1)] + [(-3*7/2)x^(-3-1)]
    - [(1*1)x^(1-1)]

    remember to be careful when working with minus signs and any number raise to the power of zero will give you 1

    therefore:

    dy/dx= 45x^2 - (21/2)x^-4 - 1

    ReplyDelete
  3. GoldfingerMarch 11, 2009 at 5:48 PM

    the final answer to solution 2 is correct but some steps are missing

    first we sub u for 6s^3+s

    which make the equation P = ln(u)

    therefore dp/du = 1/u

    but we want dp/ds
    so dp/ds = dp/du x du/ds

    now using the equation u = 6s^3+s
    du/ds = 18s^2+1

    so dp/ds = (18s^2+1)x [1/(6s^3+s)]

    or (18s^2+1)/(6s^3+s)

    ReplyDelete
  4. JohMarch 12, 2009 at 11:28 AM

    y = 15 x^3 + 7/(2x^3) - x

    the solution is wrong, when you brought the downstairs of 7/(2x^3) to upstairs. It was suppose to be (7/2)x^3 not 7 *2 x^-3, so therefore the answer would be:

    y = 15x^3 + (7/2)x^3 - x

    where dy/dx = 45x^2 - ((21/2)x^-4) - 1

    ReplyDelete
  5. ghetto_celebMarch 12, 2009 at 7:55 PM

    the solution is correct. remember when you carry a power from downstairs to upstairs if it is positive downstairs, it become negative upstairs hence the reason for 7/(2x^3) becoming (7/2)*x^-3.

    ReplyDelete
  6. small manMarch 17, 2009 at 7:44 PM

    y = log base 3 (8x^7 + x)
    u = 8 x^7 + x
    dy/dx = 56 x^6 + 1
    = (56 x^6 + 1) log base 3 e (8x^7 +x)

    can anyone correct me if i am wrong. i am not sure if it is correct.

    ReplyDelete
  7. small manMarch 17, 2009 at 8:03 PM

    joh can u explain further i dont really catch on ur explaination????

    ReplyDelete
  8. mysticwings*March 20, 2009 at 2:38 PM

    the 1st one in solution 3:

    the second line in solution 3 is correct because the 1st thing to do is to move all that is downstairs, upstairs.

    however the last line is incorrect because the person wasnt aware of police. so it should of been:

    = 45x^2 - 42x^-4 - 1

    ReplyDelete
  9. mysticwings*March 20, 2009 at 2:47 PM

    the second 1 in solution 3 is incorrect because the person did not differentiate the second term correct. they differentiated the term just as it was and made an error. this is why all terms should be carried upstairs when division is taking place. this is done to prevent errors like this one!!!

    ReplyDelete
  10. mysticwings*March 20, 2009 at 2:59 PM

    hey can someone who knows how to do problem 1 and 2 PROPERLY explain it to me, it is confusing. plzz help!!!

    ReplyDelete
  11. Kurosaki IchigoMarch 21, 2009 at 8:57 AM

    To mysticwings*, i kno that this is correct:
    y = log base 3 (8x^7 + x)

    Substituting:
    u = 8 x^7 + x
    du/dx = 56 x^6 + 1

    Rewriting the equation:
    y = log base 3u

    Then we didnt learn how to differentiate logs so i think up to here is correct.

    ReplyDelete
  12. empressApril 7, 2009 at 12:26 PM

    I really don't know how to do these questions. can someone go through one of them step by step so i can try them on my own.
    that will be very helpful.
    thanks in advance

    ReplyDelete
  13. Swanky ThingApril 8, 2009 at 12:50 PM

    I myself am lost. someone take it one step at a time plez

    ReplyDelete

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