Answer
$$ R'(y)
=\frac{-3+4\cos y}{\sin^2 y}.$$
Work Step by Step
Since $ R(y)= \frac{3\cos y-4}{\sin y}$, then using the quotient rule, the derivative is giving by
$$ R'(y)=\frac{\sin y(-3\sin y)-\cos y(3\cos y-4)}{\sin^2 y} \\
=\frac{-3\sin^2 y-3\cos^2 y+4\cos y)}{\sin^2 y}\\
=\frac{-3+4\cos y}{\sin^2 y}.$$