# How do you implicitly differentiation #1-xy = x-y#?

##### 2 Answers

You have to use the implicit function theorem (aka the Dini's theorem)

The implicit equation is

Notation:

Dini's theorem says that in every point

So,

Now we invert,

So in

Notice that we don't have an "explicit" formula for the derivatives

When we differentiate, we'll need the product rule for the second term on the left.

I use the order:

So

And