(11) Let f(x) = x^3− 1 and g(x) = 2 + 5 sin 3x. (a) What is the range of g(f(x))? Justify your answer.
(b) If h(x) = f(g(x)) compute h′(x).
(c) If t(x) = e^f(x) compute t′(x). [6 marks]
(d) Obtain f′(x) from first principles. [6 marks]
(e) Obtain the equation of the line tangent to the curve y = f(x) at x = 3.