text: prove that d/dx xⁿ = nxⁿ‾¹? prove that d/dx xⁿ = nxⁿ‾¹, for all values of n.  ^_^ rewrite x^n=e^(n*ln(x))  d(x^n)/dx=d(e^(n*ln(x))) use e^u and u =n*ln(x) => d(x^n)=(n/x)*e^(n*ln(x))= (n/x)*x^n=n*x^(n-1) qed.