Question

Use logarithmic differentiation to determine the derivative.

Answer 1

\[ f(x) = \frac {x^{2} (x-9)^{9} } { (x^2 +5)^{9} }\]

Answer 2

why does your face look like you're suffering from constipation ?

Answer 3

is math really that difficult?

Answer 4

:(

Answer 5

Rude.

Answer 6

let\[\ln f(x)=\ln\frac{x ^{2}(x-9)^{9} }{(x ^{2}+5)^{9} }\]\[=2lnx+9\ln(x-9)-9\ln(x ^{2}+5)\]
\[\frac{ f \prime(x) }{ f(x) }=\frac{ 2 }{ x }+\frac{ 9 }{ x-9 }-\frac{ 18x }{x ^{2}+5 }\]

Answer 7

Please let me know if you need me to simplify further

Answer 8

alright alright i understand so far

Answer 9

thats all?

Answer 10

take the f(x) to the RHS and simplify

Answer 11

f'(x) = \[ \frac {x^{2} (x-9)^{9} } { (x^2 +5)^{9} }\left( \frac{ 11 }{ x }-\frac{ 18 }{ x^2 +5 } \right)\]
@DominicNg I'm having a hard time simplifying

Answer 12

oh wait i think i know what i did

Answer 13

got it, thanks :D