A differential equation is an equation in which some function is related to its own derivative(s). For

each of the following functions, calculate the appropriate derivative, and show that the function

satisfies the indicated differential equation

(a) f(x) = 2e^(−3x), f^1(x) = −3*f(x)

(b) f(t) = Ce^kt, f^1(t) = k*f(t)

(c) f(t) = 1 − e^(−t), f^1(t) = 1 − f(t)