= ｢(f(x+h)·g(x+h)−f(x)·g(x))/h :h⨠0｣
= ｢(f(x+h)·g(x+h)−f(x+h)·g(x)+f(x+h)·g(x)−f(x)·g(x))/h :h⨠0｣
┅
−f(x+h)·g(x)+f(x+h)·g(x) inserted
┅
= ｢(f(x+h)·g(x+h)−f(x+h)·g(x))/h :h⨠0｣ + ｢(f(x+h)·g(x)−f(x)·g(x))/h :h⨠0｣
┅
split up into two limits
┅
= ｢f(x+h):h⨠0｣·｢(g(x+h)−g(x))/h:h⨠0｣ + ｢(f(x+h)−f(x))/h:h⨠0｣·｢g(x):h⨠0｣
= f(x)·(g(x)▽x)+(f(x)▽x)·g(x)
