Not much to do here other than take the derivative, which will require the quotient rule.

\[R'\left( t \right) = \frac{{\left( 0 \right)\left( {2\sin \left( t \right) - 4\cos \left( t \right)} \right) - \left( 1 \right)\left( {2\cos \left( t \right) + 4\sin \left( t \right)} \right)}}{{{{\left( {2\sin \left( t \right) - 4\cos \left( t \right)} \right)}^2}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{ - 2\cos \left( t \right) - 4\sin \left( t \right)}}{{{{\left( {2\sin \left( t \right) - 4\cos \left( t \right)} \right)}^2}}}}}\]