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