What is the second derivative of $f (x) = sec x$ $f(x)= sec x$ ?

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Answer 1 · 2016-02-01T11:21:21

${sec}^{3} x + {tan}^{2} x sec x$ $sec^3x+tan^2xsecx$

$\frac{d}{d x} (sec x)$ $d/(dx)(secx)$

$= s e x tan x$ $=sextanx$

$\frac{d}{d x} (sec x tan x)$ $d/(dx)(secxtanx)$

$= sec x \frac{d}{d x} (tan x) + tan x \frac{d}{d x} (sec x)$ $=secxd/(dx)(tanx)+tanxd/(dx)(secx)$

$= sec x {sec}^{2} x + tan x sec x tan x$ $=secxsec^2x+tanxsecxtanx$

$= {sec}^{3} x + {tan}^{2} x sec x$ $=sec^3x+tan^2xsecx$

What is the second derivative of f(x)= sec xf(x)=secxf(x)= sec x?