Question

If $f\left(x\right)$ is differentiable everywhere, then ${\left|f\right(x\left)\right|}^2$ is differentiable everywhere.( Enter 1 if true or 0 otherwise)

Answer 1

If $f\left(x\right)$ is differentiable everywhere then ${\left|f\left(x\right)\right|}^2$ is differentiable everywhere because

${\left|f\left(x\right)\right|}^2=f\left(x\right)\times f\left(x\right)$(The product of the two differential functions are differntiable)

$\therefore |f\left(x\right){|}^2$ is differential everywhere