Question

What is the derivative of arctan (y/x) with respect to y??

Answer 1

do you mean d(arctan(y/x)/dy ?

Answer 2

yes, I think so.....it's written d/dy arctan (y/x)

Answer 3

d/dy = 1/(1+(y/x)^2) *1/x

Answer 4

\[d/dy=1/x*1/(1+(y/x)^{2})\]

Answer 5

sorry, have that one! I meant to say with respect to x....or d/dx

Answer 6

ok

Answer 7

d/dx=\[=-y/x ^{2} * 1/(1+( y/x)^{2})\]

Answer 8

where do you get teh -y/x^2 from?

Answer 9

or rather, how??

Answer 10

you take derivative of arctan & then * derivative of (y/x)

Answer 11

the derivative of arctan is 1/1+(y/x)^2, right? and OH, use the quotient rule on the (y/x) part??

Answer 12

or product rule of ou write it y(x^-1)?

Answer 13

http://library.thinkquest.org/3616/Calc/S2/DR.html
product rule :)
I don't understand question regarding writing...?

Answer 14

d/dx=
=−y/x2∗1/(1+(y/x)2)
this is suppose to be an answer...
do you mean that you would like to write it differently? would it matter?

Answer 15

I got it...I was confused about the -1 or -y in the answer....when deriving with respect to x, you do nothing to the y....if you write it as yx^-1, then it is simply y* -1(x^-2), correct?? Which is really -1y/x^2 or -y/x^2......correct?

Answer 16

what if y is not a constant and it is a function of x
is that what you are wondering?

Answer 17

no, just how to prove the derivative of y/x step by step....

Answer 18

it's the same thing really
see:
\[=d(yx ^{-1})/dx=d(y/x)/dx=-1*y/x ^{2}=-yx ^{-2}\]
it just different ways to write the same thing

Answer 19

gotcha!!! thanks :-)

Answer 20

sure!

Answer 21

just in case y is a function of x we can say
d/dx={(y'x-y)/x^2}*(1/(1+(y/x)^2))

Answer 22

i used quotient rule to find derative of y/x
derivative of y is y'

Answer 23

yes, was trying to do it that way also... thanks!!