Find the derivative of `f(tanx)wdotrdottg(secx)a tx=pi/4,` where `f^(prime)(1)=2a n dg^(prime)(sqrt(2))=4.`

Explanation

To find the derivative of the function \( \frac{d}{dx} \left( f(\tan x) \right) \) with respect to \( \frac{d}{dx} \left( g(\sec x) \right) \) at \( x = \frac{\pi}{4} \), we will follow these steps:

### Step 1: Differentiate \( f(\tan x) \)
Using the chain rule, we have:
\[ \frac{d}{dx} f(\tan x) = f'(\tan x) \cdot \frac{d}{dx}(\tan x) \]
The derivative of \( \tan x \) is \( \sec^2 x \). Thus,
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