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f(x) as f'(x)= lim as h tends to 0 ((f(x+h)-f(x))/h)

Prove that if f(x)=x^n

then

f'(x)=nx^(n-1)

I'm confused as to how to exactly incorporate the nCr "n choose r" into this interpretation of the derivative.

Any hints or explanations would be greatly appreciated!