Question

Find dy/dx in terms of x and y

3x sin y + 2 cos y = sin x​

Answer 1

`3x\sin y+2\cos y=\sin x`

`(\mathrm d(3x\sin y+2\cos y))/(\mathrm dx)=(\mathrm d(\sin x))/(\mathrm dx)`

`(\mathrm d(3x))/(\mathrm dx)\sin y+3x(\mathrm d(\sin y))/(\mathrm dx)+(\mathrm d(2\cos y))/(\mathrm dx)=\cos x`

`3\sin y+3x\cos y(\mathrm dy)/(\mathrm dx)-2\sin y(\mathrm dy)/(\mathrm dx)=\cos x`

Solve for dy/dx :

`3\sin y+\left(3x\cos y-2\sin y\right)(\mathrm dy)/(\mathrm dx)=\cos x`

`\left(3x\cos y-2\sin y\right)(\mathrm dy)/(\mathrm dx)=\cos x-3\sin y`

`(\mathrm dy)/(\mathrm dx)=\boxed{(\cos x-3\sin y)/(3x\cos y-2\sin y)}`