Proof differentiation of functions

Reference no: EM13127777

1) Let n be a natural number, and let f: R-->R be the function f(x) :=x^n. Show that f is differentiable on R and f '(x)=nx^n-1 for all x belonging to R

(Use induction)

2) Let n be a negative integer, and let f:R - {0} -->R be the function f(x):=x^n, show that f is differentiable on R and f '(x)=nx^n-1 for all x belonging to R - {0}

(Use problem 1)

Reference no: EM13127777

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