Question

dy/dx of xy=(x^2)+(y^2)

Answer 1

x'y+xy' = 2xx' + 2yy'

Answer 2

The answer posted for this problem is (2x-y)/(x-2y)

Answer 3

can you do the implicit differentiation ? of for example
\[ \frac{d}{dy}(xy) \]

Answer 4

just use http://www.geteasysolution.com/

Answer 5

Its for a final i just wanted to understand it

Answer 6

I got the right answer i just wanted to know how that one guy got x'y+xy' = 2xx' + 2yy'

Answer 7

Since i was able to manipulate it to the correct answer

Answer 8

by the product rule
\[ \frac{d}{dx}(xy) = x \frac{d}{dx}y + y \frac{d}{dx}x \\
= x\frac{dy}{dx}+ y
\]

Answer 9

Thanks!

Answer 10

and the right-hand side is
\[ \frac{d}{dx}x^2 + \frac{d}{dx}y^2 \\= 2 x + 2y \frac{dy}{dx}\]

Answer 11

I think i just over thought it

Answer 12

ok, and to finish it (and using y' for dy/dx) btw x' in this case would mean dx/dx = 1
xy' + y = 2x + 2y y'
x y' - 2y y' = 2x -y
(x - 2y) y' = 2x -y
and
\[ y' = \frac{2x-y}{x-2y} \]