Question

If f(x)= sec x, find f"(Pi/4)

I am not sure how to take the 2nd derivative?

f'(x)= sec x tan x
f"(x)=???

Is it f"(x)= (sec x tan x)(sec^2x)???

Please Help!

Answer 1

f'(x)= sec x tan x is correct
now use the product rule

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

I will leave the subbing to you

Answer 2

What do you mean subbing? I thought that was the final answer? In the book it leaves f"(x)= - cos x for f(x)= cos x

Answer 3

Oops, sorry about that. Do you mean this:

sec^3(Pi/4) + sec(Pi/4)(tan^2(Pi/4)) =
3*sqrt(2)