Question

Find the second derivative of f(x)=sec(x).

Answer 1

The derivative of sec x is equal to sec x tan x. The derivative of the first derivative can be determined using the rule of products. The derivative is equal to sec x sec^2 x + tan x * sec x tan x. The simplified answer is sec^3 x + sec^2 x tan x equal to sec^2 x ( sec x + tanx ) 

Answer 2

Answer: $f"(x)=\sec x\tan^2 x+\sec^3 x$

Step-by-step explanation:

The given function : $f(x)=\sec x$

First we find the first derivative of the function, so differentiate both sides , with respect to x, we get

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

Now, to find the second derivative, we differentiate again it with respect to x, we get

$f"(x)=(\sec x)'\tan x+\sec x(\tan x)'\\\\\Rightarrow\ f"(x)=(\sec x\tan x)\tan x+\sec x(sec^2x)\\\\\Rightarrow\ f"(x)=\sec x\tan^2 x+\sec^3 x$

Hence, the  second derivative of $f(x)=\sec x$ is $f"(x)=\sec x\tan^2 x+\sec^3 x$