amyna
  • amyna
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
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amyna
  • amyna
|dw:1442084297389:dw|
Jhannybean
  • Jhannybean
Do you know how the chain rule works?
hartnn
  • hartnn
a possible first step would be to use \(\ln a^b = b \ln a\)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.