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    Hi, having some trouble with one of the questions in the MEI C3 A2 Pure Mathematics textbook, can anyone help me please?

    Exercise 4D pg 86 Question 1)viii)
    Differentiate:

    y=ln((x+1)/x)

    Trying to use the quotient rule, but I'm unsure about how to split the equation up [If you get what I mean].

    Thanks in advance
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    (Original post by Ash Cool 1)
    Hi, having some trouble with one of the questions in the MEI C3 A2 Pure Mathematics textbook, can anyone help me please?

    Exercise 4D pg 86 Question 1)viii)
    Differentiate:

    y=ln((x+1)/x)

    Trying to use the quotient rule, but I'm unsure about how to split the equation up [If you get what I mean].

    Thanks in advance
    You should know that \frac{d}{dx}\ln[f(x)] = \frac{f'(x)}{f(x)}.
    In this case, f(x)=\frac{x+1}{x} = 1+ \frac{1}{x}. Find f'(x) and divide it by f(x).
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    Try using this identity: ln(A/B) = ln A - ln B It'll be easier then
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    So you get the first bit where you differentiate the log?

    Spoiler:
    Show
    y = ln(f(x))
    dy/dx = f'(x)/f(x)


    and you are having trouble differentiating (x+1)/x ?
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    I understand that lna/b is the same as lna - lnb but I don't know what to to after that. I've gotten up to something like:

    y=ln((x+1)/x)
    y=ln(x+1)-ln(x)

    or when I tried it a different way:

    y=ln((x+1)/x)
    y=ln((x+1)x^-1)
    u=ln(x+1)
    v=x^-1

    then used the quotient rule to get:

    dy/dx=(((x^-1)(1/(x+1))-((ln(x+1))(-1)))/x

    Then I have no idea what to do

    [btw, sorry for the over use of brackets, I just like to be sure haha]
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    I've done it now, thanks for the help everyone
 
 
 
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Updated: October 3, 2010
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