Exercise 9

Let $f(x) = \sin(x) \cot(x)$.

1. Use the product rule to find $f'(x)$.

2. True or false: for all real numbers $x$, $f(x) = \cos(x)$.

3. Explain why the function that you found in (a) is almost the opposite of the sine function, but not quite. (Hint: convert all of the trigonometric functions in (a) to sines and cosines, and work to simplify. Think carefully about the domain of $f$ and the domain of $f'$.)