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Math Help - Differentiate the following

  1. #1
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    Differentiate the following

    i havn't done maths in awhile and when i got back into it ive totally forgot how to do these so if anyone could help me out it will be great

    so differentiate the following and simplify where appropriate

    y= x^5/(3x+4)

    y = lnx/x

    r(t) = ln(2t square root (t + 1))

    thanks
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  2. #2
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    Quote Originally Posted by helpme2009 View Post
    i havn't done maths in awhile and when i got back into it ive totally forgot how to do these so if anyone could help me out it will be great

    so differentiate the following and simplify where appropriate

    y= x^5/(3x+4)

    y = lnx/x

    r(t) = ln(2t square root (t + 1))

    thanks
    For the first one you will need the quotient rule:
    \frac{d}{dx}\frac{f(x)}{g(x)}=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}
    In this case f(x)=x^5 and g(x)=3x+4

    Then we have:
    \frac{d}{dx}\frac{x^5}{3x+4}=\frac{(5x^4)(3x+4)-(x^5)(3)}{(3x+4)^2}=...
    The rest is just simplifying.
    ---
    The second one is similar to the first one. You can do this problem using the quotient rule.
    (Note also: \ln x=\frac{1}{x})

    ---
    The third one is a combination of the chain rule and the product rule or by changing it a little bit can avoid the chain rule. (I assume that you know these two rules?)
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