Question

How do you use implicit differentiation to find dy/dx given `y^2=2+xy`?

Answer 1

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

Explanation:

Differentiate both sides of the equation with repect to `x`:

`d/dx y^2 = d/dx (2+xy)`

`2y dy/dx = y+x dy/dx`

Solve for `dy/dx`:

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

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

Answer 2

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

Explanation:

differentiate each term on both sides `color(blue)"implicitly with respect to x"`

Use the `color(blue)"product rule"` on the term xy

`rArr2ydy/dx=0+(x.dy/dx+y.1)`

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

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