## Dodo1 2 years ago f(x)=[Inx]^4

1. geerky42

Do you know chain rule? @Dodo1

2. Dodo1

Logarithmic Derivative rules that i have to use

3. Dodo1

Yes I do, f'(g(x).g(x)'

4. geerky42

Yeah. Use it. You should get 4(lnx)³ · (1/x)

5. Dodo1

6. Dodo1

its not Logarithmic Derivative is it?

7. Dodo1

@zepdrix any ideas?

8. zepdrix

Why would they want you to apply Logarithmic Differentiation to this problem? Very strange... Ok I guess we can do it though :\ Rewrite $$\large f(x)$$ as $$\large y$$. Then take the log (base e) of both sides. $\large \ln y=\ln\left[(\ln x)^4\right]$

9. Dodo1

put In to both side, ok

10. zepdrix

Using a rule of logarithms,$\large \color{royalblue}{\log(b^\color{orangered}{a})=\color{orangered}{a}\log(b)}$ We can bring that 4 out front.

11. zepdrix

This is going to be a much more difficult problem using Logarithmic Differentiation. I'm not sure why the directions would suggest you do this :) lol

12. zepdrix

$\large \ln y=4 \ln\left[\ln x\right]$

13. zepdrix

Take the derivative of both sides with respect to x. Wanna take a shot at that part? :) What do you get on the left side of the equation?

14. Dodo1

4log(x)?

15. zepdrix

whut? D:

16. geerky42

What do you get on the left side of the equation? LEFT side

17. Dodo1

oh left x/1?

18. Dodo1

No its just Y?

19. Dodo1

Im really bad at log stff!

20. Dodo1

@geerky42 ?

21. Dodo1

Oh! I see ops

22. zepdrix

y'/y

23. Dodo1

1/y' is y'/y?

24. zepdrix

$\large \frac{d}{dx}\ln y \qquad = \qquad \frac{1}{y}\cdot\frac{dy}{dx}$

25. Dodo1

thats cool!

26. Dodo1

so 1/y*dy/x= In[Inx]^4. do i use chain rule for the next step?