### Home > APCALC > Chapter 6 > Lesson 6.4.2 > Problem6-141

6-141.

The last remaining basic equation without a derivative is the equation of a circle, $x^2 + y^2 = r^2$, where $r$ is a constant. What is $\frac { d y } { d x }$ for this equation?

Recall that a circle is NOT a function.

Before differentiating, you could solve for $y$ and get

$y=\pm \sqrt{x^{2}-1}.$

Then find the derivative of each piece separately, or.....

You could use implicit differentiation!

Implicit differentiation:

$\frac{d}{dx}(x^{2}+y^{2})=\frac{d}{dx}(1)$

$\text{Now find }\frac{dy}{dx}.$