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Math Help - differnentiation problem

  1. #1
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    differnentiation problem

    Hello, I am trying to differentiate this:
    x^3cos(lnx)

    Would I be correct in using the chain rule like this? :

    3x^2(cos(lnx) * -sin(lnx) * 1/x)

    Thanks for any help.
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  2. #2
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    You need to apply the product rule as well. You can't just differentiate each term in the product individually.
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  3. #3
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    Also, you haven't correctly applied the chain rule. The derivative of cos(lnx) should just be -sin(lnx) * (1/x).
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  4. #4
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    thanks for helping.
    I have had another go at it.

    Would I be right in saying the answer is:

    3x^2cos(lnx) + x^3-sin(lnx) * 1/2
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  5. #5
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by fran1942 View Post
    thanks for helping.
    I have had another go at it.

    Would I be right in saying the answer is:

    3x^2cos(lnx) + x^3-sin(lnx) * 1/2
    Your first term is correct, the second is wrong. This problem involves a product rule with a chain rule.

    \displaystyle\frac{d}{dx}x^3 cos(ln(x))=cos(ln(x))*3x^2 + x^3 \frac{d}{dx}(cos(ln(x))

    =3x^2 cos(ln(x))-x^2sin(ln(x))
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