Question

How do you differentiate `xy=pi/6`?

Answer 1

`dy/dx=-y/x`

Explanation:

differentiate `color(blue)"implicitly with respect to x"`

Using the `color(blue)"product rule"` to differentiate the term xy

`rArr(x.dy/dx)+(y.d/dx(x))=0`

`rArrxdy/dx+y=0rArrxdy/dx=-y`

`rArrdy/dx=-y/x`