Find the derivative of the function: $(x^{2}+1) \cos x$. (Assume that $a, b, c, d, p, q, r, s$ are fixed non-zero constants and $m, n$ are integers.)

(N/A) Let $f(x) = (x^{2}+1) \cos x$.
Using the product rule for differentiation,$\frac{d}{dx}[u(x)v(x)] = u(x)v'(x) + v(x)u'(x)$:
$f'(x) = (x^{2}+1) \frac{d}{dx}(\cos x) + \cos x \frac{d}{dx}(x^{2}+1)$
$f'(x) = (x^{2}+1)(-\sin x) + \cos x(2x)$
$f'(x) = -x^{2} \sin x - \sin x + 2x \cos x$
Therefore,the derivative is $2x \cos x - (x^{2}+1) \sin x$.