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March 30, 2017

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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!

  • Calc - ,

    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

  • Calc - ,

    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

  • Calc - ,

    Oops, sorry about that. Do you mean this:

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

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