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anonymous

  • 5 years ago

Differentiate the given function: lnx^3 should the next step be 3lnx^2

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  1. apples
    • 5 years ago
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    Well, note that here you would use the chain function. The outer function is log(x) and the inner function is x^3. Noting that \[\frac{d}{dx} \left(f(g(x))\right) = f'(g(x)) \cdot g'(x)\] then you'll want to differentiate log(x) and plug x^3 into it, then multiply that by the derivative of x^3.

  2. anonymous
    • 5 years ago
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    good answer apples

  3. amistre64
    • 5 years ago
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    ln(x) dresses down to 1/x: 3ln(x)^2 ------- x

  4. apples
    • 5 years ago
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    That's not correct. You're right that d/dx log(x) = 1/x, however this yields the result \[\frac{1}{x^3} \cdot 3x^2\] which simplifies to \[\frac{3}{x}\]

  5. anonymous
    • 5 years ago
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    if you mean (lnx)^3 then amistre is right if you mean ln(x^3) then apples is right

  6. amistre64
    • 5 years ago
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    ...... oh the humanity!! ;)

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