Find the derivative of the following function: $\frac{a}{x^{4}}-\frac{b}{x^{2}}+\cos x$,where $a$ and $b$ are fixed non-zero constants.

(N/A) Let $f(x) = \frac{a}{x^{4}} - \frac{b}{x^{2}} + \cos x$.
Using the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$ and the derivative of trigonometric functions $\frac{d}{dx}(\cos x) = -\sin x$:
$f'(x) = \frac{d}{dx}(ax^{-4}) - \frac{d}{dx}(bx^{-2}) + \frac{d}{dx}(\cos x)$
$f'(x) = a(-4x^{-5}) - b(-2x^{-3}) - \sin x$
$f'(x) = -\frac{4a}{x^{5}} + \frac{2b}{x^{3}} - \sin x$.