[tex]~~~\dfrac{d}{dx}( \sec^2 x + \tan^2 x)\\\\\\=\dfrac{d}{dx}( 1+ \tan^2 x + \tan^2 x)~~~~~~~~~~~~;[\sec^2 x - \tan^2 x =1]\\\\\\=\dfrac{d}{dx}(1+2\tan^2 x)\\\\\\=0 +2 \dfrac{d}{dx} \tan^2 x\\\\\\=2 \cdot 2 \tan x \dfrac{d}{dx} \tan x\\\\\\=4 \tan x \cdot \sec^2 x\\[/tex]
