How do I differentiate f(x) = cos(x)/x?

To answer this question you need to use the quotient rule. dy/dx = (vu' - uv')/v².

^{U = cos(x) which differentiates to -sin(x) so u'= -sin(x)}

^{v = x so v' = 1}

Therefore, dy/dx = ( -xsin(x) - cos(x) ) / x²