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UPSC NDA Math Model Paper 2

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Question : 51 of 120

Marks: +1, -0

The derivative of

\sec^2

x with respect to sec x is

2 sec x
sec x
tan x
sec x tan x

Solution:

Let

u=\sec^{2}x

and

v=\sec x

Differentiating with respect to x, we get

\Rightarrow\frac{du}{dx}=\frac{d\sec^{2}x}{dx}=\frac{d\sec^{2}x}{d\sec x}\times\frac{d\sec x}{dx}

=2\sec x\times\sec x\tan x=2\sec^{2}x\tan x

Now, v = sec x

Differentiating with respect to x, we get

\Rightarrow\frac{dv}{dx}=\sec x\tan x

Now,

\frac{du}{dv}=\frac{du}{dx}\times\frac{dx}{dv}=\frac{\frac{du}{dx}}{\frac{dv}{dx}}

=\frac{2\sec x\times\sec x\tan x}{\sec x\tan x}=2\sec x

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