Question

(y/x)+(x/y)=2y calculate the derivative respect to x (implicit differentiation)

Answer 1

use quotient rule for each of the fractions
http://en.wikipedia.org/wiki/Quotient_rule

each time you differentiate a "y" term, multiply by dy/dx

Answer 2

this is going to be a drag, but we can do it if you like

Answer 3

\[(lowdhigh-highdlow)/low ^{2}\]

Answer 4

\[(x(dy/dx)-y(1))/x^2 + (y(1)-(x)(dy/dx))/y^2=2(dy/dx)\]
\[(x(dy/dx)-y)y ^{2}+(y-x(dy/dx))x ^{2}=2x ^{2}y ^{2}(dy/dx)\]
\[xy ^{2}(dy/dx)-y ^{3}+x ^{2}y-x ^{3}(dy/dx)=2x ^{2}y ^{2}(dy/dx)\]
\[dy/dx(xy ^{2}-x ^{3}-2x ^{2}y ^{{2}})=y ^{3}-x ^{2}y\]
\[dy/dx=(y ^{3}-x ^{2}y)/xy ^{2}-x ^{3}-2x ^{2}y ^{2}\]

then just reduce/factor out x's and y's