So far we’ve only differentiated functions, or relations where `y` was written *explicitly* as a function of `x`. We can also differentiate relations that aren’t functions, and they are often written *implicitly* (sometimes there is no other way). To differentiate these relations, we take the derivative of both sides and solve for the derivative that we want.

Consider the following relation:

`x^2 + y^2 = 25`.

This describes a circle centred about the origin with a radius of 5. In this relation, `y` is not a function of `x`, but we still want to find the derivative of the former with respect to the latter. We start by taking the derivative of both sides:

`d/(dx)(x^2 + y^2) = d/(dx)25`.

We can apply the sum rule on the left and the constant rule on the right:

`d/(dx)x^2 + d/(dx)y^2 = 0`.

The `x^2` term is easy, but we need the chain rule for the `y^2` term:

`2x + 2y*(dy)/(dx) = 0`.

Now we can simply solve for the derivative that has just appeared:

`(dy)/(dx) = -x/y`.

We’re done! That’s all there is to it. Try verifying this derivative by looking at the tangent slopes on a circle with a radius of 25.