Math 161

Sample First Midterm

Problem 4h

Dr. Wilson

4h. Find the first and second derivative.

Since sec x = 1/ cos x, we can use the quotient rule.

This is often written as

f'(x) = sec x tan x

Since we know how to differentiate both the secant and tangent as a result of this problem, we can use the product rule to get the second derivative

f"(x) = (sec x tan x)tan x + sec x sec2x

= sec x tan2x + sec3x