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    hey
    how do you differentiate y= 3ln(x^2+1)
    I think I need to use the product rule but Im not sure how.. :/
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    (Original post by Kiimii)
    hey
    how do you differentiate y= 3ln(x^2+1)
    I think I need to use the product rule but Im not sure how.. :/
    Let y = x^2 +1

    So differentiate 3 ln y which gives 3/y.

    Then differentiate y with respect to x i.e. differentiate x^2 +1 which gives 2x

    Then multiply together to give the answer: 6x/(x^2 +1)

    This is the Chain Rule in operation not the product rule.
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    (Original post by Kiimii)
    hey
    how do you differentiate y= 3ln(x^2+1)
    I think I need to use the product rule but Im not sure how.. :/
    You don't need to use the product rule.

    There's a formula for differentiating logarithmic functions.
    It's \dfrac {d (ln(f (x))}{dx}= \dfrac {f'(x)}{f (x)}

    The guy above answer is correct so just apply this formula to future questions. But this is a short cut method, what he did was the long way.
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    (Original post by pvaz6965)
    Let y = x^2 +1

    So differentiate 3 ln y which gives 3/y.

    Then differentiate y with respect to x i.e. differentiate x^2 +1 which gives 2x

    Then multiply together to give the answer: 6x/(x^2 +1)

    This is the Chain Rule in operation not the product rule.
    oh ok thank you!
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    (Original post by ServantOfMorgoth)
    You don't need to use the product rule.

    There's a formula for differentiating logarithmic functions.
    It's \dfrac {d (ln(f (x))}{dx}= \dfrac {f'(x)}{f (x)}

    The guy above answer is correct so just apply this formula to future questions. But this is a short cut method, what he did was the long way.
    thanks!!
 
 
 
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