find the derivative: f(x)=(ln x^2)^3 The answer is: 24(lnx)^2/x i have no idea where to start! plz help!!

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find the derivative: f(x)=(ln x^2)^3 The answer is: 24(lnx)^2/x i have no idea where to start! plz help!!

Mathematics
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Do you know how the chain rule works?
a possible first step would be to use \(\ln a^b = b \ln a\)

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actually, the chain rule is \(\sf \frac{d}{dx} (f(g(h(x))))= f'(g(h(x))) \cdot g'(h(x)) \cdot h'(x)\)
ok so when i used the chain rule, so far i have: 3(lnx^2)^2 (1/x * 2x)
is that the correct way to start?
whats the derivative of ln x^2 ?
right its 1/x^2 *2x
think chain rule example: if I wanted derivative if sin^2 x it would be 2 sin x* (derivative of sin x) because derivative of x^2 is 2x
so try once more, whats the derivative of ln x^2 ?
a much better start would be to use \(\Large \ln x^2 = 2\ln x \)
2/x ?
thats the derivative of 2 ln x starting again, f(x) = (2 ln x)^3 = 2^3 (ln x)^3 makes sense??
2lnx/x
2^3 = 8 applying chain rule for (ln x)^3 is easier. try it
3(lnx)^2 *( 1/x)
perfect! now multiply that with 8
oh okay! got it Thanks so much!! :)
welcome ^_^

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