Consider the function $f(x) = \tan(x)$, and remember that $\tan(x) = \displaystyle{\frac{\sin(x)}{\cos(x)}}$.

(a) What is the domain of $f$?

(b) Andre computes $f'(x)$ using the quotient rule. Which of the following is a possible correct answer?

(c) Berenice simplifies Andre's correct answer using the Fundamental Trigonometric Identity. Which of the following is a correct answer?

(d) Corey simplifies Berenice's correct answer using another trigonometric Identity. Which of the following is a correct answer?

(e) For what values of $x$ is $f'(x)$ defined?