A Quick Proof of the Power Rule (4.1.2)

Question 1

• In math, it is not enough to find patterns. Once you find one, it is necessary to prove that it holds in general. To prove the power rule for integer exponents, use the binomial theorem to express the general case.

Answer 1

• In math, it is not enough to find patterns. Once you find one, it is necessary to prove that it holds in general. To prove the power rule for integer exponents, use the binomial theorem to express the general case.

Question 2

• The power rule states that if N is a rational number, then the function f(x) = x^N is differentiable and f’(x) = Nx^(N-1).

Answer 2

• The power rule states that if N is a rational number, then the function f(x) = x^N is differentiable and f’(x) = Nx^(N-1).