Explore BrainMass
Share

Explore BrainMass

    Proof differentiation of functions

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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)

    © BrainMass Inc. brainmass.com October 10, 2019, 4:48 am ad1c9bdddf
    https://brainmass.com/math/derivatives/proof-differentiation-functions-477912

    Solution Preview

    We have:
    (1.1)
    Where n is a positive integer
    The derivative is defined as
    (1.2)
    For we have:
    (1.3)
    For we have:

    (1.4)
    We assume that
    (1.5)
    And we show by induction that if this is true then
    (1.6)

    We ...

    Solution Summary

    The expert examines proof differentiation of functions.

    $2.19