Question

Example secx Differentiate f (x) = secx/ 1+tan x​

Answer 1

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$\pink{ \tt{ \implies \: f^{1} (x) = \frac{( 1+ tan \: x) \frac{d}{dx} (sec \: x) - sec \: x \frac{d}{dx}(1 +tan \: x) }{(1 + { \tan \: x})^{2} } }}$

${ \tt{ \implies \: \frac{sec \: x(tan \: x - 1)}{(1 + tan) {}^{2} } }}$

${ \tt{ \implies \frac{(1 + \: tan \: x)sec \: x \: tan \: x \: - sec \: x \times {sec}^{2} \: x }{(1 + {tan \: x})^{2} } }}$

${ \tt{ \implies\frac{sec \: x \: (tan \: x + ta {n}^{2} x - sec^{2}x) }{(1 + tan \: s){}^{2} } }}$

$</strong><strong>{ \tt{ \implies \: \frac{sec \: x(tan \: x - 1)}{(1 + \: tan \: {x})^{2} } }}</strong><strong>$

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