f(g(x))▽x
= ｢(f(g(x+h))−f(g(x)))/h :h⨠0｣
= ｢(f(g(x+h))−f(g(x)))/(g(x+h)−g(x))·(g(x+h)−g(x))/h :h⨠0｣
= ｢(f(g(x+h))−f(g(x)))/(g(x+h)−g(x)) :h⨠0｣·｢(g(x+h)−g(x))/h :h⨠0｣
ᐥ
Let g(x+h)−g(x) = t, then ｢t :h⨠0｣ = 0 and g(x+h) = g(x) + t.
｢(f(g(x+h))−f(g(x)))/(g(x+h)−g(x)) :h⨠0｣
= ｢(f(g(x)+t)−f(g(x)))/t :t⨠0｣
ᐥ
= ｢(f(g(x)+t)−f(g(x)))/t :t⨠0｣·｢(g(x+h)−g(x))/h :h⨠0｣
= (f(g(x))▽g(x))·(g(x)▽x)
