Question

How do you find `dy/dx` by implicit differentiation given `x/y+3y=2`?

Answer 1

`dy/dx=-y/(3y^2-x)`

Explanation:

`x/y+3y=2`

`rArrx/y=2-3y`

differentiate all terms on both sides `color(blue)"implicitly with respect to x"`

`"differentiate "x/y" using the " color(blue)"quotient rule"`

#rArr(y.1-x.dy/dx)/(y^2)=0-3.dy/dx#

`rArry-xdy/dx=-3y^2dy/dx`

`rArrdy/dx(3y^2-x)=-y`

`rArrdy/dx=-y/(3y^2-x)`