anonymous
  • anonymous
Differentiate the given function: lnx^3 should the next step be 3lnx^2
Mathematics
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anonymous
  • anonymous
Differentiate the given function: lnx^3 should the next step be 3lnx^2
Mathematics
jamiebookeater
  • jamiebookeater
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apples
  • apples
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.
anonymous
  • anonymous
good answer apples
amistre64
  • amistre64
ln(x) dresses down to 1/x: 3ln(x)^2 ------- x

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apples
  • apples
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 \[\frac{3}{x}\]
anonymous
  • anonymous
if you mean (lnx)^3 then amistre is right if you mean ln(x^3) then apples is right
amistre64
  • amistre64
...... oh the humanity!! ;)

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