Question

Differentiate (3y/x^2)^x, no using computers to help.

Answer 1

time limit: 5 mins, starting now.

Answer 2

time limit extended 5 mins more.

Answer 3

a quiz for us?

Answer 4

you should probably specify which variable you want to differentiate with respect to.

Answer 5

X

Answer 6

5 minutes extra now :P lol

Answer 7

I'm dying.

Answer 8

sorry to hear that

Answer 9

Imagine not using a computer when differentiating.

Answer 10

I got my answer because it's similar to the last. I'm not sure it's right, but I wouldn't want to kill your fun if you think I'm cheating.

Answer 11

you can type it down

Answer 12

...

Answer 13

I assume that is a yes...

Answer 14

How did you start?

Answer 15

ln y = x ln (3y/x^2)

Answer 16

y'/y=a lot of stuff

Answer 17

I didn't take the log, but that would've helped.
actually now I'm getting\[y=\sqrt{\frac{3y}{e^3}}\]do you know the other is right?

Answer 18

no wait

Answer 19

that should be an x under the radical

Answer 20

Lemme type the question as clearly as I could, since I didn't

Answer 21

y = (3y/x^2)^x, differentiate y.

Answer 22

Im getting confused.

Answer 23

I'm feeling that I'm getting there.

Answer 24

Me too, I keep getting different answers.
I tried to ignore all the parts that can't be zero to cut down on work, but I think I made a mistake.

Answer 25

You tried to ignore the parts that can't be zero?
?

Answer 26

looks like you need to use implicit differentiation

Answer 27

\[y=(\frac{3y}{x^2})^x\]
Take natural log of both sides
note:also remember derivative of y is y'
\[\ln(y)=x \ln(\frac{3y}{x^2})\]
\[\ln(y)=x [\ln(3y)-\ln(x^2)]\]
\[\ln(y)=x[\ln(3)+\ln(y)-2 \ln(x)]\]
\[\frac{y'}{y}=x[0+\frac{y'}{y}-2 \cdot \frac{1}{x}]+1[\ln(3)+\ln(y)-2 \ln(x)]\]
\[\frac{y'}{y}=x \cdot \frac{y'}{y}-2+\ln(3)+\ln(y)-2 \ln(x)\]

Answer 28

I am.

Answer 29

\[\frac{y'}{y}-\frac{x y'}{y}=-2+\ln(3)+\ln(y)-2 \ln(x)\]
\[y'(\frac{1-x}{y})=-2 +\ln(3)+\ln(y)-2 \ln(x)\]

Answer 30

\[y'=\frac{y}{1-x}(-2+\ln(3)+\ln(y)-2\ln(x))\]

Answer 31

now if its multiple choice I will leave the dressing up to you

Answer 32

dressing up as in simplifying

Answer 33

y' = y(ln(3y/x^2)-2)?

Answer 34

that give the same answer, but is not what I have...

Answer 35

mine should have yielded what I wrote the second time, I am confused.

Answer 36

y'/y = d/dx (x) ln(3y/x^2) + d/dx (ln(3y/x^2)) (x)