Question

se logarithmic differentiation to find dy/dx.
y = (x^2 − 64/x^2 + 64) , x > 8
dy/ dx =

can someone please help me?

Answer 1

\[\ln(y)=\ln|\frac{x^2-64}{x^2+64}|\]
\[\ln(y)=\ln|x^2-64|-\ln|x^2+64|\]
\[\frac{y'}{y}=\frac{2x-0}{x^2-64}-\frac{2x+0}{x^2+64}\]

Answer 2

\[y'=y(\frac{2x}{x^2-64}-\frac{2x}{x^2+64})\]

Answer 3

\[y'=\frac{x^2-64}{x^2+64} (\frac{2x}{x^2-64}-\frac{2x}{x^2+64})\]

Answer 4

log dif, is sweet

Answer 5

\[y'=\frac{2x}{x^2+64}-\frac{2x(x^2-64)}{(x^2+64)^2}\]

Answer 6

\[y'=\frac{2x(x^2+64)-2x(x^2-64)}{(x^2+64)^2}\]

Answer 7

is that the answer?

Answer 8

wow your so good at this

Answer 9

so thats the final answer?

Answer 10

you might want to check my arithmetic

Answer 11

so 126x/(x^2+64)^2 is the answer

Answer 12

i don't have a calculator with me

Answer 13

hmm 64*4 is 256

Answer 14

yep it should be 256 lol

Answer 15

omg lol

Answer 16

\[y'=\frac{2(2(64)x)}{(x^2+64)^2}=\frac{4(64)x}{(x^2+64)^2}=\frac{256x}{(x^2+64)^2}\]

Answer 17

hmm everything else seems ok..should is imply the bottom

Answer 18

simpliify*

Answer 19

what?

Answer 20

simplify the bottom?

Answer 21

could u quickly check the arimthmatic, using a online claculutor?

Answer 22

like factor the bottom out?

Answer 23

the bottom is factored

Answer 24

do you multiply
don't make something more ugly

Answer 25

do you mean multiply*

Answer 26

ok..so do u think thats right now..do u mind checking your work over i did but maybe you might catch a mistake

Answer 27

yeh

Answer 28

liek the bets way towrite it out..its a online quiz:(

Answer 29

well i like the way we have our answer right now

Answer 30

if you really want to check you work you can use wolfram

Answer 31

i'm gonna go eat

Answer 32

hmmm oki then.