Tangent Lines

The graph of the function

$f(x) = \sqrt{1 - x^2}$

is shown below.

$x = cos (\theta)$
$y = sin (\theta)$

For the function

$f(x) = \sqrt{1 - x^2}$

The derivative is

$f'(x) = \dfrac {-x} {\sqrt{1 - x^2}}$