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Math Help - functions using chain rule

  1. #1
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    functions using chain rule

    i have the function
    log (x^2+1)
    e

    and i believe the answer is

    2x
    x^2+1

    but i am not sure what steps to take to get the answer, can anyone help.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bart 1000 View Post
    i have the function
    log (x^2+1)
    e

    and i believe the answer is

    2x
    x^2+1

    but i am not sure what steps to take to get the answer, can anyone help.
    use the chain rule. it says \frac d{dx} f(g(x)) = f'(g(x)) \cdot g'(x)

    here your f(x) = \ln x and your g(x) = x^2 + 1

    what this translates to for the natural log is: \frac d{dx} \ln u = \frac {u'}u, where u is a function of x

    that is, you take the derivative as if the x^2 + 1 was a single variable, and then multiply by its derivative, which is 2x, when done
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  3. #3
    Moo
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    Hello,
    Quote Originally Posted by bart 1000 View Post
    i have the function
    log (x^2+1)
    e

    and i believe the answer is

    2x
    x^2+1

    but i am not sure what steps to take to get the answer, can anyone help.
    Yes it is the answer
    But I don't understand why you want the steps... How did you get the answer, since it is correct ?

    In general, let f(x) be a function, f(x) > 0

    The derivative of \ln (f(x)) is, by using chain rule, \frac{f'(x)}{f(x)}
    And hence your result.
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