Question

find dx/dy for the following equations
1.) y = square root of 3 (x+1)/x-1)

Answer 1

\[\sqrt[3]{X+1/x-1}\]

Answer 2

2) y = cos(lnX)

Answer 3

ok

Answer 4

let me have a look to this closely

Answer 5

please tke your time

Answer 6

babz83 is smilbourn your mother?

Answer 7

cbrt((x+1)/(x-1)) right?

Answer 8

change the radical to its proper exponent form

[ (x+1)/(x-1) ]^(1/3) and work thru

Answer 9

this aint gonna be nice with my formatting off

Answer 10

lets start with the ^1/3; power rule says bring it down and -1

Answer 11

@owlfred...nope remember she said she got an A in calc.... i would not be posting these questions

Answer 12

(1/3) [ (x+1)/(x-1) ]^(-2/3) and out pops the innards for the chain rule

Answer 13

Dx(x+1)/(x-1) = (x-1)(1) - (x+1)(-1) // (x-1)^2 by quotient rule

Answer 14

simplify to: 2x/(x-1)^2 right?

Answer 15

put it all together to go: 2x/3(x-1)^2) [ (x-1)/(x+1) ]^(2/3)

Answer 16

am following u amistre

Answer 17

let me just digest it!

Answer 18

\[\frac{2x}{3(x-1)^2}\left(\frac{x-1}{x+1}\right)^{2/3}\]right?

Answer 19

ill type it in the latex stuff fo try to make it easier to follow

Answer 20

nope

Answer 21

\[\sqrt[3]{x+1/x-1}\]

Answer 22

ah i get it thats after removing the cube root

Answer 23

\[\sqrt[3]{\frac{x+1}{x-1}}\]
\[Dx\left(\frac{x+1}{x-1}\right)^{1/3}\]
\[\frac{1}{3}\left(\frac{x+1}{x-1}\right)^{-2/3}Dx(\frac{x+1}{x-1})\]
so far

Answer 24

-2/3 just flips it all over and goes positive again right?

Answer 25

right

Answer 26

\[\frac{1}{3}\left(\frac{x-1}{x+1}\right)^{2/3}Dx(\frac{x+1}{x-1})\]

\[... Dx(\frac{x+1}{x-1})=\frac{bt'-b't}{b^2}\]
\[... \frac{(x-1)(1)-(x+1)(-1)}{(x-1)^2}\]
\[... \frac{(x-1)+(x+1)}{(x-1)^2}\]
\[... \frac{x-1+x+1}{(x-1)^2}\]
\[... \frac{2x}{(x-1)^2}\]

Answer 27

\[\frac{1}{3}\left(\frac{x-1}{x+1}\right)^{2/3}\frac{2x}{(x-1)^2}\]
are all the parts, just simplify as wanted

Answer 28

i see a spot i missed; (x-1) has a derivative if 1, not -1

Answer 29

thnks a lot

Answer 30

i see i have a lot of serious reading to do

Answer 31

\[... \frac{(x-1)(1)-(x+1)(1)}{(x-1)^2}\]
\[... \frac{x-1-x-1}{(x-1)^2}\]
\[... \frac{-2}{(x-1)^2}\]
\[\frac{1}{3}\left(\frac{x-1}{x+1}\right)^{2/3}\frac{-2}{(x-1)^2}\]
thats proper, or should be better at least :)