Skriv \displaystyle x^n=x\cdot x^{n-1}. Vi får \displaystyle D(x^n)= D(x\cdot x^{n-1}) = D(x)\cdot x^{n-1} + xD(\cdot x^{n-1})= 1\cdot x^{n-1} + x(n-1)x^{n-2} = nx^{n-1}.
