hi, we already know a function is
(A) differentiable at if
exists.
now consider f:R R, f(x) = , for some N E N. Using the definition of (A), how can we prove that f is differentiable and that f'(x) = ?
help would be greatly appreciated here. thank you
identity: .
now that we have that identity.. we deduce
i think this is right to my knowledge.
but this is what i'm having difficulty understanding.
(1) where does the identity come from.. and how do you explain this identity's expansion?
(2) finally, how does that identity apply to the expansion of the limit, finally arriving at the right answer...
haha genius. i get the gist of it.
the only parts that are bugging me are:
1) on the expansion of a^n - b^n.. where does the inital (a - b) come from?
2) why does that expansion equal na^n-1?
is there something to show that when the terms add up they equal na^n-1?
and would this all be sufficient to say that we've "proved" f is differentiable?
Just multiply out the paranthesis and everything cancels out. Or use long division.1) on the expansion of a^n - b^n.. where does the inital (a - b) come from?
Because there are terms all equal to .why does that expansion equal na^n-1?
is there something to show that when the terms add up they equal na^n-1?