If x3−x≥0⇒cos|x3−x|=cos(x3−x) x3−x<0⇒cos|x3−x|=cos(x3−x) Similarly b|x|sin|x3+x|=bxsin(x3+x) for all x ∊ R ∴f(x)=acos(x3−x)+bxsin(x3+x) which is composition and sum of differentiable functions therefore always continuous and differentiable