Chapter 2.4, Problem 40ES

Suppose that the function $f$ is differentiable everywhere and $F\left(x\right)=xf\left(x\right)$ .

(a) Express ${{F^{\prime }}^{\prime }}^{\prime }\left(x\right)$ in terms of $x$ and derivatives of $f$ .

(b) For $n\ge 2$ , conjecture a formula for $F^{\left(n\right)}\left(x\right)$ .