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Math Help - Differentiation Question

  1. #1
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    Differentiation Question

    Differentiate lnx/x^5

    Using the quotient rule I got a final answer of x^4-lnx5x^4/x^10

    First of all is this correct, if so is it in its simplest form.

    Please help, thanks.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by haku View Post
    Differentiate lnx/x^5

    Using the quotient rule I got a final answer of x^4-lnx5x^4/x^10

    First of all is this correct, if so is it in its simplest form.

    Please help, thanks.
    it is correct, but it is not the simplest form. factor out the x^4 in the numerator and then cancel it into the denominator.

    by the way, learn to use parentheses. you should have typed: (x^4 - 5x^4 * lnx)/(x^10)
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  3. #3
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    Thanks for that help. Sorry for not using parenthesis. I now realise what I typed makes no sense!
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  4. #4
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    For this example here:

    (x^4 + 3)^3 cos2x

    When differentiating would you use a combination of the chain rule and the product rule, giving an answer of:
    (12x^2(x^4+3)^2(cos2x)) + ((x^4+3)^3(sin2x)).

    Does this look okay?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by haku View Post
    For this example here:

    (x^4 + 3)^3 cos2x

    When differentiating would you use a combination of the chain rule and the product rule, giving an answer of:
    (12x^2(x^4+3)^2(cos2x)) + ((x^4+3)^3(sin2x)).

    Does this look okay?
    that's not correct
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  6. #6
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    Could you please help me get on the right track then?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by haku View Post
    Could you please help me get on the right track then?
    recall that by the product rule we have that \frac d{dx}f(x)g(x) = f'(x)g(x) + f(x)g'(x)

    here we have f(x) = \left( x^4 + 3 \right)^3 \implies f'(x) = 12x^3 \left( x^4 + 3 \right)^2 by the chain rule

    and g(x) = \cos 2x \implies g'(x) = -2 \sin 2x also by the chain rule

    now just put the pieces together. with practice you will be able to do all this in one line without splitting up the parts like this, so keep at it
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  8. #8
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    Thanks again for your help.
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