What is the derivative of f(tan x) w.r.t. g(sec x) at x = , if f'(1) = 2 and g'(√2) = 4?

  1. √2
  2. √3
  3. None of these.

Answer (Detailed Solution Below)

Option 2 :
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

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Concept:

Derivatives of Trigonometric Functions:

Chain Rule of Derivatives:

  • .
  • .


Calculation:

Let v = f(tan x) and u = g(sec x).

Now,  = f'(tan x).sec2 x and  = g'(sec x).tan x.sec x.

And 

⇒ 

Substituting the given values f'(1) = 2 and g'(√2) = 4, we get:

 = 1/√2.

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