Thread: Differentiation

Please can you help, i can't figure it out.

Show that the derivative of:

x + y = x/y

can be written as

y^3/x^2(2-y)

The dfferentiation is really simple and i got
(1-y)/(x + 2y) when i times the left hand side by y before differentiating. However i cannot make it into that form!

Hello, mathshelpneeded!

Show that the derivative of: .x + y .= .x/y
. . can be written as: .y' .= .y³/x²(2 - y)

The differentiation is really simple and i got: .y' .= .(1 - y)/(x + 2y) . [1]
However i cannot make it into that form!

I'm not sure how to get it into that form naturally,
. . but I can hammer it into that form . . .


From the original equation, we have:
. . xy + y² .= .x . → . y² .= .x(1 - y) .[2] . → . 1 - y .= .y²/x . [3]

The original equation is: .x + y .= .x/y
Add y to both sides: .x + 2y .= .x/y + y .= .(x + y²)/y
. . From [2]: .x + 2y .= .[x + x(1 - y)]/y . → . x + 2y .= .x(2 - y)/y . [4]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . y²/x . . . . . . . y³
Substitute [3] and [4] into [1]: .y' .= . ------------ .= .-----------
. . . . . . . . . . . . . . . . . . . . . . . . . . . x(2 - y)/y . . . .x²(2 - y)