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

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Answer 1 · 2018-07-16T10:25:40

$f''(x)=sec x(\sec^2 x+\tan^2 x)$

given function:

$f(x)=\sec x$

Differentiating w.r.t. $x$ as follows

$\frac{d}{dx}f(x)=\frac{d}{dx}(\sec x)$

$f'(x)=\sec x\tan x$

Again, differentiating $f'(x)$ w.r.t. $x$ , we get

$\frac{d}{dx}f'(x)=\frac{d}{dx}(\sec x\tan x)$

$f''(x)=\sec x\frac{d}{dx}\tan x+\tan x\frac{d}{dx}\secx$

$=\sec xsec^2 x+\tan x\sec x\tan x$

$=sec^3 x+\sec x\tan^2 x$

$=sec x(\sec^2 x+\tan^2 x)$

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