## 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!!

1. amyna

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2. anonymous

Do you know how the chain rule works?

3. hartnn

a possible first step would be to use $$\ln a^b = b \ln a$$

4. hartnn

actually, the chain rule is $$\sf \frac{d}{dx} (f(g(h(x))))= f'(g(h(x))) \cdot g'(h(x)) \cdot h'(x)$$

5. amyna

ok so when i used the chain rule, so far i have: 3(lnx^2)^2 (1/x * 2x)

6. amyna

is that the correct way to start?

7. hartnn

whats the derivative of ln x^2 ?

8. amyna

right its 1/x^2 *2x

9. 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

10. hartnn

so try once more, whats the derivative of ln x^2 ?

11. hartnn

a much better start would be to use $$\Large \ln x^2 = 2\ln x$$

12. amyna

2/x ?

13. hartnn

thats the derivative of 2 ln x starting again, f(x) = (2 ln x)^3 = 2^3 (ln x)^3 makes sense??

14. amyna

2lnx/x

15. hartnn

2^3 = 8 applying chain rule for (ln x)^3 is easier. try it

16. amyna

3(lnx)^2 *( 1/x)

17. hartnn

perfect! now multiply that with 8

18. amyna

oh okay! got it Thanks so much!! :)

19. hartnn

welcome ^_^