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astraxan [27]
2 years ago
13

Derive this with respect to x

Formula1" title=" \frac{3}{(1 + secx) } " alt=" \frac{3}{(1 + secx) } " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Elenna [48]2 years ago
8 0

~~~~\dfrac{d}{dx} \left(\dfrac{3}{1 + \sec x} \right)\\\\\\=3 \dfrac{d}{dx} \left( \dfrac 1{ 1+ \sec x} \right)\\\\\\=3 \dfrac{d}{dx} (1+ \sec x)^{-1}\\\\\\=3 (-1) (1 + \sec x )^{-1 -1} \dfrac{d}{dx}( 1 + \sec x)\\\\\\=-3(1 + \sec x)^{-2}  ( 0 + \sec x  \tan x)\\\\\\=-\dfrac{3\sec x \tan x}{(1 + \sec x)^2}

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