Найти dy/dx и d^2y/dx^2 для функции y=sinx/x

Question

Найти dy/dx и d^2y/dx^2 для функции y=sinx/x

Answer 1

       (sin x)' * x - sin x * (x)'      x * cox x - sin x

y' = ---------------------------- = ----------------------

                     x²                                x²

          x * cos x - sin x           ( x * cos x - sin x )' * x² - (x * cos x - sin x) * (x²)'  

y'' = ( --------------------- ) ' = -------------------------------------------------------------- =

                    x²                                             ( x² )²

 (-x * sin x) * x² - (x * cos x - sin x) * 2 * x      - x² * sin x - 2 * x * cos x + 2 * sin x  

--------------------------------------------------- = --------------------------------------------

                             x⁴                                                           x³