Question

What is the implicit derivative of `1= ln(xy)`?

Answer 1

`dy/dx=-y/x`

Explanation:

Know that `d/dx[ln(u)]=(u')/u`.

`d/dx[1=ln(xy)]`

`0=(d/dx[xy])/(xy)`

`0=(y+xdy/dx)/(xy)`

`0=y+xdy/dx`

`xdy/dx=-y`

`dy/dx=-y/x`