Verified Answer :

meerkat18


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 )

JeanaShupp

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

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