Exercise 3: Let f(x) = x", with n E N. (a) Find a formula for f"(x) (b) Hard] Find a formula for f (k) (x) for all k E N. Remark: I am unsure of how far we will get in class, and don't want the...

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Extracted text: Exercise 3: Let f(x) = x", with n E N. (a) Find a formula for f"(x) (b) Hard] Find a formula for f (k) (x) for all k E N. Remark: I am unsure of how far we will get in class, and don't want the problem to be too hard. You may freely use that: f'(x) = nx"-1, and that if g(x) = c - f(x) (with c a constant), then g'(x) = c- f'(x) Remark: In case this wasn't said in class, recall f(k)(x) is the k-th derivative of f at x, e.g., it is the derivative of f(-1) at r, which is then defined inductively with f(1(x) more, f" (x) = f(2)(x) and f" (x) = f(3)(x) are alternative notations for the small-order derivatives. = f'(x). Further- Hint: Your answer will depend on if n > k or if n <>