Differentiate $e^{x} \cos x$ with respect to $x$.

Explanation

1. 01

   Product rule: $(uv)' = u'v + uv'$, with $u = e^{x}$ and $v = \cos x$.

2. 02

   $(e^{x})(\cos x) + (e^{x})(- \sin x) = - e^{x} \sin x + e^{x} \cos x$.