## Calculus (3rd Edition)

$cos^{2}(x)-sin^{2}(x)$
Using the product rule for differentiation, or $[uv]'=u'v+vu'$, the derivative of $sin(x)cos(x)$ is $sin(x)[cos(x)]'+[sin(x)]'cos(x)$, or $cos^{2}(x)-sin^{2}(x)$.