[tex]3x\sin y+2\cos y=\sin x[/tex]
[tex]\dfrac{\mathrm d(3x\sin y+2\cos y)}{\mathrm dx}=\dfrac{\mathrm d(\sin x)}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm d(3x)}{\mathrm dx}\sin y+3x\dfrac{\mathrm d(\sin y)}{\mathrm dx}+\dfrac{\mathrm d(2\cos y)}{\mathrm dx}=\cos x[/tex]
[tex]3\sin y+3x\cos y\dfrac{\mathrm dy}{\mathrm dx}-2\sin y\dfrac{\mathrm dy}{\mathrm dx}=\cos x[/tex]
Solve for dy/dx :
[tex]3\sin y+\left(3x\cos y-2\sin y\right)\dfrac{\mathrm dy}{\mathrm dx}=\cos x[/tex]
[tex]\left(3x\cos y-2\sin y\right)\dfrac{\mathrm dy}{\mathrm dx}=\cos x-3\sin y[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\boxed{\dfrac{\cos x-3\sin y}{3x\cos y-2\sin y}}[/tex]
