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anonymous
 one year ago
Calculus  calculate the derivative from the given information: F(u)=u^3 and g(x)=u= (x+4)/(x2), find (f o g) ' (3)
The answer is 882, but I cannot figure out how to arrive at this value.
anonymous
 one year ago
Calculus  calculate the derivative from the given information: F(u)=u^3 and g(x)=u= (x+4)/(x2), find (f o g) ' (3) The answer is 882, but I cannot figure out how to arrive at this value.

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Empty
 one year ago
Best ResponseYou've already chosen the best response.0Give it your best shot and I'll help you out since you likely have most of the steps right already.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03(u)^2 * x2 * 1x+4*1 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f ' u=3u^2 f ' g(x)= 3[(x+4)/(x2)]^2 g ' (x)= 1/1 ??

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1\[f(g(x)) = f\left(\frac{x+4}{x+2}\right)\] and \((f(g(3)))' = f'(g(3)) \cdot g'(3)\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1baby steps. Check it out.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1You're trying to find \((f(g(x)))'\) when \(x=3\) , therefore you have to apply the chain rule. \[(f(g(x)))' = f'(g(x)) \cdot g'(x)\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1So whats the easiest portion to solve for? that would be \(g(3)\) and \(g'(x)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not seeing it It would be helpful if you could brake it down more for me

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1\[g(3) = \frac{3+4}{32} = \frac{7}{1} = 7\]\[\begin{align} g(x) = (x+4)(x2)^{1} &\implies g'(x) = 1(x2)^{1} (x2)^{2}(1)(x+4) \\&\implies g'(x) = \frac{6}{(x2)^2} \\ &\implies g'(3) =\frac{6}{(\color{red}{3}2)^2} \\&\implies g'(3) = 6 \end{align}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Now im a little confused with the whole f(u)=u\(^3\) part.... \(x=u\)?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0\[\large\rm f(\color{orangered}{u})=(\color{orangered}{u})^3\]And \(\large\rm \color{orangered}{g(x)=u=\frac{x+4}{x2}}\) So then,\[\large\rm f(\color{orangered}{u})=f(\color{orangered}{g(x)})=\left(\color{orangered}{\frac{x+4}{x2}}\right)^3\]Ya I think maybe you forgot to chain rule little panda?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Oh thats what it meant...ok

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0\[\large\rm \frac{d}{dx}f(g(x))=3\left(\frac{x+4}{x2}\right)^2\color{royalblue}{\frac{d}{dx}\left(\frac{x+4}{x2}\right)}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0`g ' (x)= 1/1 ??` No. I guess that's where you ran into trouble. Apply quotient rule or something similar. :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Aw he ran off, prolly had to get some more bamboo
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