Question

Given ycos(x^2) = xcos(y^2), use implicit differentiation to find dy/dx.

Answer 1

phewww i hope this right ;)

Answer 2

at the 1st steps, u were mistake... so on also be mistake :)
look at the left side, it should be y'cos(x^2) - 2xysin(x^2)

Answer 3

you right

Answer 4

oops

Answer 5

so the rest is screwed off lol

Answer 6

when differentiate of y, so cos(x^2) will be coeff, doesnt it

Answer 7

lol, yes

Answer 8

but the right side I think i got it?

Answer 9

yeah, for right side very good i thnk..

Answer 10

lol

Answer 11

np, sometimes i have done mistake too like u :)

Answer 12

\[\frac{ \cos(y^2) +2xysin(x^2)}{ \cos(x^2)+2xysin(y^2)}\]

is this what you get?

Answer 13

i got dy/dx = (2xysin(x^2) + cos(y^2)) / (2xysin(y^2) + cos(x^2))
if i dont mistake also :)

Answer 14

yeeh then we got it ;;)..long arse problem (*^_~*)

Answer 15

hoho... but i think asker be angry if we just discuss the answer only without show the steps for solution :D

Answer 16

\[y'\cos(x^2)-ysin(x^2)(2x)=\cos(y^2)+x(-\sin(y^2))(2y)y'\]
\[y'\cos(x^2)-2xysin(x^2)=\cos(y^2)-2xysin(y^2)y'\]
\[y'\cos(x^2)+2xysin(y^2)y'=\cos(y^2)+2xysin(x^2)\]
\[y'(\cos(x^2)+2xysin(y^2))=\cos(y^2)+2xysin(x^2)\]
\[y'=\frac{ \cos(y^2)+2xysin(x^2) }{ \cos(x^2)+2xysin(y^2) }\]