If `f(x)=xcosx`, find `f''(x)`.

Explanation

Using the product rule, we have
`f'(x)=x(d)/(dx)(cosx)+cosx(d)/(dx)(x)=-xsinx+cosx`
To find `f''(x)`, we differentiate `f'(x)`:
`f''(x)=(d)/(dx)(-xsinx+cosx)`
`=-x(d)/(dx)(sinx)+sinx(d)/(dx)(-x)+(d)/(dx)(cosx)`
`=-xcosx-sinx-sinx=-xcosx-2sinx`