Question

How do you find the derivative of `x^2 - y^2 = 16`?

Answer 1

I assume that we want to find `dy/dx`

`x^2 - y^2 = 16`

Our choices are: solve for `y` (make the function(s) explicit and differentiate

OR

leave the function `=f(x)` implicit and use implicit differentiation.

Because this question was posted under Implicit Differentiation, we'll do that.

`x^2 - y^2 = 16`
so the derivative with respect to `x` of the left side equals the derivative with respect to `x` of the right.

We write:

`d/dx(x^2 - y^2) = d/dx(16)`

Now find the derivatives (remembering that `y` is some unknown function of `x`, so we need the chain rule to differentiate `y^2`

`2x-2y dy/dx = 0`

Solve for `dy/dx = x/y`