How to differentiate cos(x)/x^2? - Applying the Quotient Rule

Suppose we have the function

f(x) = \frac {\cos x}{x^2}

We note that f is composed of the division of 2 different functions of x, and as such, we have to use the quotient rule in order to find the derivative.

The Quotient Rule is given by:

f' = \frac {vu' - uv'}{v^2}

So if we let...

u = cos(x)
v = x²

then...

u' = -sin(x)
v' = 2x

And applying the Quotient Rule, we get...

f' = \frac {x^2\cdot -\sin x - \cos x\cdot 2x}{(x^2)^2}