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AmTran_Bus
 one year ago
My bus is going to quit if it does not get some help.
AmTran_Bus
 one year ago
My bus is going to quit if it does not get some help.

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AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0I just need to know which of those choices matches my answer.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1You got your answer using WolframAlpha? lol.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Do you know how to use logarithmic differentiation?

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0Yes. It always gives it in a different form, but awesome to check your answer.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1You just need to go ahead and apply logarithmic differentiation. \[\ln y = 5\ln (3x+1)+ 6\ln(x^42)\]Now taking derivative of both sides; \[\dfrac{y'}{y} = \cdots~?\]

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1\[\dfrac{\mathrm d}{\mathrm dx}~~~5\ln (3x+1)+ 6\ln(x^42)=~?\]

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Yeah just use WolframAlpha.

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0ok http://www.wolframalpha.com/input/?i=d%2Fdx+5ln%283x%2B1%29%2B6ln%28x%5E42%29

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Now multiply both sides by y. Then we can replace y to whether it equals to; \[y' = \dfrac{15~y}{1+3 x}+\dfrac{24~ x^3~y}{x^42} \]Since we are given that \[y = (3x+1)^5~(x^42)^6\] Using our simple algebra skill, we have \[y' = \dfrac{15~\left((3x+1)^5~(x^42)^6\right)}{1+3 x}+\dfrac{24~ x^3~\left((3x+1)^5~(x^42)^6\right)}{x^42}\\~\\~\\\phantom{y'} = \boxed{15~ (3x+1)^4~(x^42)^6+24~ x^3~(3x+1)^5~(x^42)^5}\]

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0Thanks so much you will never know.
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