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    I know if you have ln[f(x] you differentiate it by using:

    f'(x)/f(x)

    but what if you have

    I tried to use the above rule but I am not getting the correct answer. Am I using the correct method?
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    (Original post by GPODT)
    I know if you have ln[f(x] you differentiate it by using:

    f'(x)/f(x)

    but what if you have

    I tried to use the above rule but I am not getting the correct answer. Am I using the correct method?
    Change of base rule.
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    I like to move it move it, she like to move it move it, we like to MOVE IT!
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    Use chain rule. Let u = the bit inside your log. Then do dy/dx = du/dx * dy/du
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    (Original post by Ateo)
    Change of base rule.
    I have used this before but can you elaborate because I am slightly confused..
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    (Original post by GPODT)
    I have used this before but can you elaborate because I am slightly confused..
    logax = ln(x)/ln(a)
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    (Original post by joostan)
    logax = ln(x)/ln(a)
    What base do we change it to?
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    (Original post by GPODT)
    What base do we change it to?
    You want to convert to ln, so that you can apply rules of calculus. Above is the specific change of base formula to do so
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    (Original post by GPODT)
    I know if you have ln[f(x] you differentiate it by using:

    f'(x)/f(x)

    but what if you have

    I tried to use the above rule but I am not getting the correct answer. Am I using the correct method?
    Is your log the natural log (ln) or log to another base?

    Regardless, you still use the chain rule for this problem.
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    (Original post by joostan)
    You want to convert to ln, so that you can apply rules of calculus. Above is the specific change of base formula to do so
    (Original post by davros)
    Is your log the natural log (ln) or log to another base?

    Regardless, you still use the chain rule for this problem.
    Yes this is the natural log. Apologies for the confusion, Wolfram Alpha interpreted ln as log..

    I used the chain rule (probably incorrectly). So I differentiated x+(1+x2)0.5 and divided this differential by x+(1+x2)0.5
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    (Original post by GPODT)
    Yes this is the natural log. Apologies for the confusion, Wolfram Alpha interpreted ln as log..

    I used the chain rule (probably incorrectly). So I differentiated x+(1+x2)0.5 and divided this differential by x+(1+x2)0.5
    This should give you the correct answer.
    Also the equation you have been given is equivalent to arcsinh(x)
    Your formula book should have the derivative of arcsinh(x) for you to check with.
 
 
 
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