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5hassay
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Homework Statement
Use the Principle of Mathematical Induction and the Product Rule to prove the Power Rule when n is a positive integer.
Homework Equations
Dxxn = nxn-1
Dx(fg) = fDxg + Dxfg
The Attempt at a Solution
In summary,
Dxxn = nxn-1
Dxxk = kxk-1
Dxxk+1 = (k+1)x(k+1)-1
Dx(xkx) = (k+1)xk
xkDxx + Dxxkx = (k+1)xk
xk + kxk-1x = (k+1)xk
xk + kxk = (k+1)xk
(k+1)xk = (k+1)xk
Therefore, Dxxn = nxn-1 is valid for all positive integers n.
EDIT: Oh, and much appreciation for any help!