Simplify[D[((a x)/(b+x)),x]]

Simplify[D[((a b)/(((b+x))^2)),b]]

Manipulate[Plot[{((a x)/(b+x)),((a b)/(((b+x))^2))},{x,0,.4},PlotRange->{-.002,0.1},PlotStyle->{Black,Red},AxesLabel->{N,R},Epilog->{{Arrow[{{.01,((3 a)/4)},{.01,(a/2)}}],Arrow[{{.01,((3 a)/4)},{.01,a}}]},Text[Style["50%",Black],{0.02,.75 a}],Text[Style["S",Blue,Medium],{-0.004,a}],Text[Style["c",Green,Medium],{b+.001,-.0015}],{Red,PointSize[Large],Point[data]},{Blue,Dashed,Line[{{0,a},{.3,a}}]},{Green,Dashed,Line[{{0,(a/2)},{b,(a/2)}}],Line[{{b,(a/2)},{b,0}}]}}],Text[Style["S",Blue,Medium],{-0.004,a}],Text[Style["c",Green,Medium],{b+.001,-.0015}]}],{{a,0.0358, "Maximum, S"},0.015,0.045, Appearance-> "Labeled"},{{b,0.021, "Half-saturation value, c"},0.01,0.2, Appearance-> "Labeled"}]

Manipulate[Plot[{((a x)/(b+x)),((a b)/(((b+x))^2))},{x,0,6},PlotRange->{-.002,0.2},PlotStyle->{Black,Red},AxesLabel->{N,Text["dR/dN, R"]}],{{a,0.1, "Maximum, S"},0.1,0.2, Appearance-> "Labeled"},{{b,1, "Half-saturation value, c"},1,3, Appearance-> "Labeled"}]