Question

f(x)=sec(x) what is f"(pi/4)? Explain procedure

Answer 1

f(x)=sec(x)


f'(x)=sec(x)*tan(x)


f''(x)=d/dx(sec(x))*tan(x)+sec(x)*(d/dx)(tan(x))


f''(x)=sec(x)*tan(x)*tan(x)+sec(x)*sec^2(x)


f''(x)=sec(x)*tan^2(x)+sec^3(x)


f''(pi/4)=sec(pi/4)*tan^2(pi/4)+sec^3(pi/4)


f''(pi/4)=sqrt(2)*(1)^2+(sqrt(2))^3


f''(pi/4)=sqrt(2)+2sqrt(2)


f''(pi/4)=3*sqrt(2)

Answer 2

\[f(x)= (\cos(x))^{-1}\]

Answer 3

use chain rule