Find the second order derivatives of the functions given.
`x.cos x`

Explanation

Let `y=x.cos x`
Differentiating w.r.t. x,

`dy/dx=(d(x.cosx))/dx`

Using Product Rule
As `(uv)'=u'v+v'u`

`dy/dx=(d(x))/(dx)*cosx+(d(cosx))/(dx).x`

`dy/dx=cosx+(-sinx).x`

`dy/dx=cosx-xsinx`

Again Differentiating w.r.t. x,

`d/dx(dy/dx)=(d(cosx-xsinx))/dx`

`(d^2y)/(d^2x)=(d(cosx))/dx-(d(xsinx))/dx`

Using product rule in `xsinx`

`(d^2y)/(d^2x)=-sinx-((d(x))/(dx).sinx+(d(sinx))/(dx).x)`

`(d^2y)/(d^2x)=-sinx-(sinx+cosx.x)`

`(d^2y)/(d^2x)=-sinx-sinx-xcosx`

`(d^2y)/(d^2x)=-xcosx-2sinx`