Question 1 What is wrong with the following argument claiming to prove that d dx 1/x = -1/12 There are actually two errors, but you only need to find one. Proof: Let f(x) = 1/x. Then 1 = f(x)x. It follows by Theorem 3.2.6 that d d 0 = 1 = dx (f(x)x) = of'(x) +f(x)-x = xf(x)+f(x) It follows that of'(x) = -f(x) and, recalling the definition of f(x), yields that rf'(x) = -1/r. Solving for f'(x) yields that d 1/x = f'(x) = -1/x2. dx