Answer
$$\left( {\text{a}} \right)dy = \left( {12{x^2} - 14x} \right)dx{\text{ and }}\left( {\text{b}} \right)dy = \left( {\cos x - x\sin x} \right)dx$$
Work Step by Step
$$\eqalign{
& \left( {\text{a}} \right)y = 4{x^3} - 7{x^2} \cr
& {\text{Calculate }}\frac{{dy}}{{dx}} \cr
& \,\,\,\frac{{dy}}{{dx}} = 12{x^2} - 14x \cr
& {\text{Then}} \cr
& \,\,dy = \left( {12{x^2} - 14x} \right)dx \cr
& \cr
& \left( {\text{b}} \right)y = x\cos x \cr
& {\text{Calculate }}\frac{{dy}}{{dx}} \cr
& \,\,\,\frac{{dy}}{{dx}} = x\left( { - \sin x} \right) + \cos x \cr
& {\text{Then}} \cr
& \,\,dy = \left( {\cos x - x\sin x} \right)dx \cr
& \cr
& \left( {\text{a}} \right)dy = \left( {12{x^2} - 14x} \right)dx{\text{ and }}\left( {\text{b}} \right)dy = \left( {\cos x - x\sin x} \right)dx \cr} $$
