HOW DERIVE THE Differentiation of a simple power FORMULA

Question

(Xⁿ+Δx)ⁿ-xⁿ=

Answer 1

One can use the binomial theorem to expand the nth power of the sum in parentheses.

 

I assume that this is in connection with taking the limit of a Difference Quotient, with Δx as denominator.

 

The result will be, of course that if f(x) = xⁿ then f'(x) = nx^n-1.