Suppose n is a negative integer and f(x) = xⁿ. Use the following steps to prove that f'(a) = na^{n - 1}, which means the Power Rule for positive integers extends to all integers.

a. Assume that m = - n, so that m > 0. Use the definition

Simplify using the factoring rule (which is valid for n > 0)

b. Use this result to find d/dx (x^-7) and d/dx (1/x¹⁰). 

x" = lim a" lim f' (a) " " ( )(x" -1 + x" ? + ... a)(x"-1 + x"a + .. + xa"-2 + a"-1) in