f(x)=ax^n ⇒ f'(x)=anx^(n-1)の証明
f'(x)=lim[⊿x→0]f(x+⊿x)-f(x)/⊿x
=lim[⊿x→0]a(x+⊿x)^n-ax^n/⊿x
=lim[⊿x→0]a[x^n+nC1{x^(n-1)}⊿x+nC2{x^(n-2)}(⊿x)^2・・・+(⊿x)^n]-ax^2/⊿x
=lim[⊿x→0]a[nC1{x^(n-1)}⊿x+nC2{x^(n-2)}(⊿x)^2・・・+(⊿x)^n]-/⊿x
=lim[⊿x→0]a⊿x[nC1{x^(n-1)}+nC2{x^(n-2)}⊿x・・・+(⊿x)^n-1]/⊿x
=lim[⊿x→0]a[nC1{x^(n-1)}+nC2{x^(n-2)}⊿x・・・+(⊿x)^n-1]
=a(nC1)x^(n-1)
=anx^(n-1) //