Question

How do you use implicit differentiation to find `(dy)/(dx)` given `xy=1`?

Answer 1

`dy/dx=-y/x`

Explanation:

We have to use the `color(blue)"product rule"` for xy and note that the derivative of a constant is zero.

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(d/dx(y)=dy/dx)color(white)(a/a)|)))`

Differentiate with respect to x.

`rArrx.dy/dx+y.1=0rArrx.dy/dx=-yrArrdy/dx=-y/x`