If `y=[3x+2][2x-1]`, then find `(dy)/(dx)`.

Explanation

Here, `u=3x+2`, `v=2x-1`.
Differentiating both sides, we get
`(dy)/(dx)=(d)/(dx)[3x+2][2x-1]`
Using product rule, we get
`(d[uv])/(dx)=u(dv)/(dx)+v(du)/(dx)`
`(dy)/(dx)=[3x+2](d)/(dx)[2x-1]+[2x-1](d)/(dx)[3x+2]`
`=[3x+2][2]+[2x-1]3`
`=6x+4+6x-3=12x+1`