19.Ya.3 Generalized Derivatives

\ (\ underline {\ text {Condition:} \ \) Show that the next display is differentiated and find its strong derivative: \ [\ Begin {Array} F: C [0.1] \ RIGHTARROUR C [0,1], \ QUAD F (x (t)) = \ int_ {0}^{t} k (x (s) d s \\ \ \ \ & N C^{1} [0.1] \ RIGHT). \ end {Array} \]