If y2=p(x) is a polynomial of degree 3, then what is 2ddx[y3d2ydx2] equal to?

[c] Given that y2=p(x)Differentiating$\Rightarrow 2yy1=p\prime \left(x\right)\left[herey1=dydx\right]$⇒2y1=p′(x)y$D\iff erentiat\in gaga\in ,$⇒2y2=yp′′(x)−p′(x)y1y2,[y2=d2ydx2]$\Rightarrow 2y2=yp\prime \prime \left(x\right)-p\prime \left(x\right).p\prime \left(x\right)2yy2$=2y2p′′(x)−p′(x))22y3$\Rightarrow 2y3y2=12\left[2y2p\prime \prime \left(x\right)-\left(p\prime \left(x\right)\right)2\right]$⇒2y3y2=12[2p(x)p′′(x)−(p′(x))2]$\Rightarrow 2ddx\left(y3y2\right)$=12[2p′(x)p′′(x)+2p(x)p′′′(x)−2p′(x)p′′(x)]$=p\left(x\right)p\prime \prime \prime \left(x\right)$