What is the second derivative of?

X^2 • lnX

I have to find the second derivative. 

For the first derivative I have: 2x • 1/x 

For the second Im stuck at: 2

Any help is much appreciated!

2 Answers

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  • 8 years ago
    Favorite Answer

    1/x = x^(-1)

    The derivative of that is -x^(-2)

    But your first derivative is wrong.

    Given f(x) = g(x) * h(x)

    f'(x) = g(x) * h'(x) + g'(x) * h(x)

    Here, g(x) = x^2

    g'(x) = 2x

    h(x) = ln(x)

    h'(x) = 1/x

    f'(x) = x^2 * 1/x + 2x * ln(x)

    f'(x) = x + 2x * ln(x)

    f''(x) = 1 + (2 * ln(x) + 2x * 1/x)

    f''(x) = 1 + 2 * ln(x) + 2

    f''(x) = 3 + 2 * ln(x)

  • JoAn
    Lv 4
    8 years ago

    y = x²(ln x)

    using product rule

    y' = (2x)(ln x) + x²/x

    y' = (2x)(ln x) + x

    y'' = 2(ln x) + 2x/x + 1

    y'' = 2(ln x) + 2 + 1

    y'' = 2(ln x) + 3

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