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amyna
 one year ago
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!!
amyna
 one year ago
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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Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0Do you know how the chain rule works?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.3a possible first step would be to use \(\ln a^b = b \ln a\)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.3actually, the chain rule is \(\sf \frac{d}{dx} (f(g(h(x))))= f'(g(h(x))) \cdot g'(h(x)) \cdot h'(x)\)

amyna
 one year ago
Best ResponseYou've already chosen the best response.1ok so when i used the chain rule, so far i have: 3(lnx^2)^2 (1/x * 2x)

amyna
 one year ago
Best ResponseYou've already chosen the best response.1is that the correct way to start?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.3whats the derivative of ln x^2 ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.3think 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

hartnn
 one year ago
Best ResponseYou've already chosen the best response.3so try once more, whats the derivative of ln x^2 ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.3a much better start would be to use \(\Large \ln x^2 = 2\ln x \)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.3thats the derivative of 2 ln x starting again, f(x) = (2 ln x)^3 = 2^3 (ln x)^3 makes sense??

hartnn
 one year ago
Best ResponseYou've already chosen the best response.32^3 = 8 applying chain rule for (ln x)^3 is easier. try it

hartnn
 one year ago
Best ResponseYou've already chosen the best response.3perfect! now multiply that with 8

amyna
 one year ago
Best ResponseYou've already chosen the best response.1oh okay! got it Thanks so much!! :)
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