Calculus Homework

Question

Let f(x)= cx+ ln(cos x). For what value of c is f'(pi/4)=1?

c=

Answer 1

f(x) = cx + ln(cosx)

f'(x) = c - sinx / cosx = c - tanx

f'(π/4) = c - tan(π/4) = c - 1

f'(π/4) = 1 when c - 1 = 1. So, c = 2.