Question

can someone help me with partial derivatives?

y= (LK)/(K+2L)

derivative of Y in respect to L and derivative of Y in respect to K

Answer 1

So when you take the partial of y w.r.t L you treat everything like a constant except L (and well y)

Answer 2

yeah i know that

Answer 3

You also need to apply quotient rule since you have a quotient.

Answer 4

\[y_L=\frac{(LK)_L \cdot (K+2L) - (LK) \cdot (K+2L)_L}{(K+2L)^2}\]

Answer 5

let me go straight to the pointi have to get this \[\frac{ derivative y respect \to L }{ derivative of Y respect \to K }\]

which is supposed to be
\[\frac{ K^2 }{ 2L^2 }\]

but i'm getting instead
\[\frac{ 2L^2 }{ K^2 }\]

Answer 6

Did you apply quotient rule? I actually already applied the quotient rule and used little symbols there or notated what needed to be taken derivative of. Right now I'm not seeing how we are to got the 2L^2 on bottom.

Answer 7

the good news is that the book is correct: K^2 / (2 L^2)

Answer 8

yeah, i know... but that's what i'm getting in the book.
i'm doing math for economics Y is the production function and i have to find the MRTS

Answer 9

so, why is the book correct?

Answer 10

what do you get for dy/dL ?

Answer 11

4KL +4L^2

Answer 12

use Mya's post

Answer 13

dy/dk =\[k^2+4KL + 4L^2\]

Answer 14

i'm still getting the same thing T_T

Answer 15

can you do just one step? using the quotient rule ?

Answer 16

ie. what is the numerator of dy/dL

Answer 17

don't bother simplifying.

Answer 18

dy/dl= \[\frac{ K.(K+2L)-2.(LK) }{ K^2+4KL+4L^2 }= \frac{K^2+2KL-2KL }{ K^2+4KL+4L^2 }= 4KL +4L^2\]

Answer 19

ahh too late

Answer 20

the top simplifies to k^2

Answer 21

\[\frac{5}{5+9} \neq 9\]

Answer 22

and I would leave the bottom as (k+2L)^2 (because it will cancel with the bottom from dy/dK)

Answer 23

It looks like you canceled the some addends from top and bottom
and left the bottom as the top

Answer 24

You can cancel common factors

Answer 25

\[\large \dfrac{k^2}{k^2+4KL+4L^2} \ne \dfrac{1}{4KL+4L^2} \ne 4KL+4L^2\]

Answer 26

but not common addends

Answer 27

yes, whatever you did to simplify is way wrong. Better debug that. in the mean time you should just get
\[ \frac{K^2}{(K+2L)^2 } \]

Answer 28

I assume you notice that in the top 2KL - 2KL is 0

Answer 29

oh waw that was a bad mistake

Answer 30

thank you guys, i was really confused, i always mix the cancellation laws

Answer 31

The "laws" also work for numbers. so if you try a similar problem with numbers, and you do something wrong, it will be obvious it did not work.