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|proof=
<tex dpi=150>\frac{\partial^n(x^a)}{\partial x^n} =a\times\frac{\partial^{n-1}(x^{a-1})}{\partial x^{n-1}}=a(a-1)\times\frac{\partial^{n-2}(x^{a-2})}{\partial x^{n-2}}</tex>
:<tex dpi=150>=a(a-1)\cdots (a-n+2)\times\frac{\partial^{n-(n-1)}(x^{a-(n-1)})}{\partial x^{n-(n-1)}}=(a)_n\,\, x^{a-n}</tex>
}}
