The derivative of $f(\tan x)$ with respect to $g(\sec x)$ at $x=\frac{\pi}{4}$, where $f^{\prime}(1)=2$ and $g^{\prime}(\sqrt{2})=4$, is

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Analyzing +4 | -1

The derivative of

f(\tan x)

with respect to

g(\sec x)

x=\frac{\pi}{4}

, where

f^{\prime}(1)=2

and

g^{\prime}(\sqrt{2})=4

, is

View answer and explanation

Correct option: A

\frac{1}{\sqrt{2}}

Option A (

\frac{1}{\sqrt{2}}

) is correct because after applying the chain rule and simplifying, the derivative evaluates to

\frac{1}{\sqrt{2}}

x = \frac{\pi}{4}

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