Question

what is the derivative of sec²x

Answer 1

1/cos2x is the derivation

Step-by-step

Answer 2

The derivative is $\frac{d}{dx}(\sec^2 x)=2\sec^2 x \tan x$

Step-by-step explanation:

Given : Expression $\sec^2 x$.

To find : What is the derivative of expression ?

Solution :

The derivative form of expression is $\frac{d}{dx}(\sec^2 x)$

Applying chain rule,

$\frac{d}{dx}(\sec^2 x)=2\sec x\frac{d}{dx}\sec x$

$\frac{d}{dx}(\sec^2 x)=2\sec x \sec x\tan x$

$\frac{d}{dx}(\sec^2 x)=2\sec^2 x \tan x$

Therefore, the derivative is $\frac{d}{dx}(\sec^2 x)=2\sec^2 x \tan x$

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