Question

f(x)=[Inx]^4

Answer 1

Do you know chain rule? @Dodo1

Answer 2

Logarithmic Derivative rules that i have to use

Answer 3

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

Answer 4

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

Answer 5

is that answer?

Answer 6

its not Logarithmic Derivative is it?

Answer 7

@zepdrix any ideas?

Answer 8

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.
\[\large \ln y=\ln\left[(\ln x)^4\right]\]

Answer 9

put In to both side, ok

Answer 10

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.

Answer 11

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

Answer 12

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

Answer 13

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?

Answer 14

4log(x)?

Answer 15

whut? D:

Answer 16

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

LEFT side

Answer 17

oh left x/1?

Answer 18

No its just Y?

Answer 19

Im really bad at log stff!

Answer 20

@geerky42 ?

Answer 21

Oh! I see ops

Answer 22

y'/y

Answer 23

1/y' is y'/y?

Answer 24

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

Answer 25

thats cool!

Answer 26

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