Results 1 to 5 of 5

Math Help - College exam questions

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    6

    College exam questions

    Hello my fellow mathematicians,

    I joined the forum today, and I hope to integrate well with this forum. I love science subjects and have made an attempt in doing Biology, Physics, Chemistry and Maths.
    I'am in urgent need for help in Mathematics as my college midterm exams are getting nearer (12 days left). I intend on using this thread for posting questions that have significantly hindered my progress:

    Here goes:

    Differentiating exponentials and logarithms:
    Question:
    Q1, Given that y = 5/1+e^3x, find the value of dy/dx when x = 0.

    Q2,Defferentiate each of the following functions with respect to x.

    a, 3lnx^-2
    b, ln(x^2+x-2)
    c, ln(x(x+1))
    d, ln 2x+1/3x-1

    Trignometry:
    Solve the equation sin2@ = 4sin(@-60), show that 2 . 3cos@ = sin@. Hence find the value of @ such that 0<@<360.


    Thank you

    Regards
    pA
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Passive_absorber View Post
    ...
    Here goes:

    Differentiating exponentials and logarithms:
    Question:
    Q1, Given that y = 5/1+e^3x, find the value of dy/dx when x = 0.

    ...
    I assume that you mean:

    f(x)=\dfrac5{1+e^{3x}} = 5\left( 1+e^{3x} \right)^{-1} If so, use chain rule to get the derivation:

    f'(x)=5\cdot (-1) \cdot \left( 1+e^{3x} \right)^{-2} \cdot e^{3x} \cdot 3 = - \dfrac{15e^{3x}}{\left( 1+e^{3x} \right)^{2}}

    Thus f'(0)=- \dfrac{15e^{0}}{\left( 1+e^{0} \right)^{2}}=-\dfrac{15}4

    For the next 4 questions use the property that \dfrac{d(\ln(x))}{dx}=\dfrac1x and the chain rule.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Passive_absorber View Post
    Hello my fellow mathematicians,

    I joined the forum today, and I hope to integrate well with this forum. I love science subjects and have made an attempt in doing Biology, Physics, Chemistry and Maths.
    I'am in urgent need for help in Mathematics as my college midterm exams are getting nearer (12 days left). I intend on using this thread for posting questions that have significantly hindered my progress:
    Don't do that, rather post one question per thread. Otherwise the thread will become unweildy and difficult to follow/make sense of.

    CB
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2008
    Posts
    6
    I assume that you mean:
    Correct. By the way, how do you write the whole thing like that. MS word does not have mathematical syntax.

    If so, use chain rule to get the derivation:



    Thus

    For the next 4 questions use the property that and the chain rule.
    Alright thanks for the help, but I have trouble understanding the chain rule used here. Oh and can this:



    be used with the chain rule together? I always thought they were seperately done. Oh and please can someone tell me the solution to the Trignometry problem.

    Don't do that, rather post one question per thread. Otherwise the thread will become unweildy and difficult to follow/make sense of.

    CB
    Sure thing. I'll keep that in mind.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Passive_absorber View Post
    Correct. By the way, how do you write the whole thing like that. MS word does not have mathematical syntax.
    Have a look here: http://www.mathhelpforum.com/math-he...-tutorial.html

    Alright thanks for the help, but I have trouble understanding the chain rule used here. Oh and can this:



    be used with the chain rule together? I always thought they were seperately done. .........What do you mean by that?

    ...
    I'm going to demonstrate b):

    f(x)=\ln(x^2+x-2)~\implies~f'(x)= \underbrace{\dfrac1{x^2+x-2}}_{\text{der.\ outer\ fct.}}\cdot \underbrace{(2x+1)}_{\text{der.\ inner\ fct.}} = \dfrac{2x+1}{x^2+x-2}

    der. outer fct. means derivation of the outer function
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: March 31st 2011, 11:06 PM
  2. A Few College Level Math Questions...
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 28th 2010, 07:35 PM
  3. College Algebra II questions.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 24th 2010, 05:24 AM
  4. A few College Algebra questions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 26th 2008, 04:44 PM
  5. 4 college algebra questions
    Posted in the Algebra Forum
    Replies: 3
    Last Post: July 3rd 2006, 09:11 PM

Search Tags


/mathhelpforum @mathhelpforum