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Which of the following is false given the following function?

$$y=f(x)=\tan x$$

$f'(x)=\sec^2 x$

$y'=\sec^2 x$

$\cfrac{dx}{dy}=\sec^2 x$

$\cfrac{d}{dx}(f(x))=\cfrac{1}{\cos^2 x}$