The derivative of $f(\sec x)$ with respect to $g(\tan x)$ at $x=\frac{\pi}{4}$, where $f^{\prime}(\sqrt{2})=4$ and $g^{\prime}(1)=2$, is
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Logic Tip: Notice how the inputs for $f'$ and $g'$ in the given information precisely match the values of $\sec(\pi/4)$ and $\tan(\pi/4)$. If they didn't match, you wouldn't be able to solve the problem! This is an excellent self-checking mechanism during an exam to confirm you are evaluating the chain rule correctly.