9/6 Worksheet
1. Find f0(x)for each of the following f.
(a) f(x) = sin(x+x2).
(b) f(x) = xln x−x.
(c) f(x) = ex/(1+cos2x).
Solution.
(a) By the chain rule:
f0(x)=(2x +1)cos(x+x2).
(b) By the product rule:
f0(x) = ln x+x(1/x) − 1=ln x.
(c) By the quotient, chain, and power rules:
f0(x) = (1+cos2x)·ex−ex·(2cos x)·(− sin x)
(1+cos2x)2.
Questions to think about. What are the functions sin xand cos x? What is ln x? What is
the number e?
