f(x)=[Inx]^4

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Do you know chain rule? @Dodo1
Logarithmic Derivative rules that i have to use
Yes I do, f'(g(x).g(x)'

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Yeah. Use it. You should get 4(lnx)³ · (1/x)
is that answer?
its not Logarithmic Derivative is it?
@zepdrix any ideas?
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. \[\large \ln y=\ln\left[(\ln x)^4\right]\]
put In to both side, ok
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.
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
\[\large \ln y=4 \ln\left[\ln x\right]\]
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?
4log(x)?
whut? D:
What do you get on the left side of the equation? LEFT side
oh left x/1?
No its just Y?
Im really bad at log stff!
Oh! I see ops
y'/y
1/y' is y'/y?
\[\large \frac{d}{dx}\ln y \qquad = \qquad \frac{1}{y}\cdot\frac{dy}{dx}\]
thats cool!
so 1/y*dy/x= In[Inx]^4. do i use chain rule for the next step?

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