3) Differentiation D: F[t] ---> F[t], is linear and satisfies Dt¹ = nt¹-1. It satisfies the usual rules for derivatives. Let f € F[t] be monic. We write f for Df. (a) Let c E F be a root of f. With p = t - c, show that f (c) #0 iff ep(f) = 1. Suppose that F contains Q, the rational numbers. (b) Show that gcd (f, f) = 1 iff Iff f = rad(f), ep(f) ≤1 i.e. V primes p of F[t]

Let f (z) = (7z + 9) (i – 2). What is the real part of the derivative f' (1 + i)?

Q8: Find the second derivative of the function: f(x) = x2 + e* +1 Select one: O a f"(x) = 2x + e* O b. f"(x) = 3+ e* f"(x) = 2x + e* + 1 C. d. f"(x) = 2 + e*

Q8: Find the second derivative of the function: f(x) = x2 + e* +1 Select one: f"(x) = 3 + e* a. O b. f"(x) = 2x + e* + 1 c. f"(x) = 2x +e* с. O d. f"(x) = 2 + e*