Functions of the form x^n, where n=1,2,3..are often called power functions. The first two questions below revisit work we did earlier in Chapter 1, and the following questions extend those ideas to higher powers of n. a. Use the limit definition of the derivative to find f'(x) for f(x) = x^2 b. Use the limit definition of the derivative to find f'(x) for f(x) = x^3. c. Use the limit definition of the derivative to find f'(x) for f(x) = x^4. ((a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4) d. Based on your work above, what do you conjecture is the derivative of f(x) = x^5? Of f(x) = x^{13}? f. Conjecture a formula for the derivative of f(x) = x^n that holds for any positive integer n. That is, given f(x) = x^n where n is a positive integer, what do you think is the formula for f'(x)