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

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geerky42
 2 years ago
Best ResponseYou've already chosen the best response.1Do you know chain rule? @Dodo1

Dodo1
 2 years ago
Best ResponseYou've already chosen the best response.0Logarithmic Derivative rules that i have to use

geerky42
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah. Use it. You should get 4(lnx)³ · (1/x)

Dodo1
 2 years ago
Best ResponseYou've already chosen the best response.0its not Logarithmic Derivative is it?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Why 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. \[\large \ln y=\ln\left[(\ln x)^4\right]\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Using a rule of logarithms,\[\large \color{royalblue}{\log(b^\color{orangered}{a})=\color{orangered}{a}\log(b)}\] We can bring that 4 out front.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2This 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

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2\[\large \ln y=4 \ln\left[\ln x\right]\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Take 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?

geerky42
 2 years ago
Best ResponseYou've already chosen the best response.1What do you get on the left side of the equation? LEFT side

Dodo1
 2 years ago
Best ResponseYou've already chosen the best response.0Im really bad at log stff!

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2\[\large \frac{d}{dx}\ln y \qquad = \qquad \frac{1}{y}\cdot\frac{dy}{dx}\]

Dodo1
 2 years ago
Best ResponseYou've already chosen the best response.0so 1/y*dy/x= In[Inx]^4. do i use chain rule for the next step?
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