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Math Help - Derivatives

  1. #1
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    Derivatives

    If I have f(x)=(x^4)ln(x^2+2), how do I find the derivative?

    My thought:

    Take the 1st x der. of 2nd + 2nd x der. of 1st?

    (x^4) x (1/x^2+2) + ln(x^2+2) x (4x^3)

    Which would then equal ????
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  2. #2
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    Quote Originally Posted by tradar View Post
    If I have f(x)=(x^4)ln(x^2+2), how do I find the derivative?

    My thought:

    Take the 1st x der. of 2nd + 2nd x der. of 1st?

    (x^4) x (1/x^2+2) + ln(x^2+2) x (4x^3)

    Which would then equal ????
    You are close. You just forgot to use the chain rule.

    \frac{d}{dx} \ln(x^2+2)=\frac{2x}{x^2+2}

    Besides that you are good. What do you mean "which would equal"?
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  3. #3
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    Quote Originally Posted by tradar View Post
    If I have f(x)=(x^4)ln(x^2+2), how do I find the derivative?

    My thought:

    Take the 1st x der. of 2nd + 2nd x der. of 1st?

    (x^4) x (1/x^2+2) + ln(x^2+2) x (4x^3)

    Which would then equal ????
    x^4 \cdot \frac{2x}{x^2+2} + 4x^3 \cdot \ln(x^2+2)
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