Differentiate secx by first principle.


Let us consider

sec x= 1/cos x

By quotient rule derivative of secx = 1/cosx

⇒ \(\frac{\frac{d}{dx}\times 1 – \frac{d}{dx} cos x \times 1}{\left ( cosx \right )^{2}}\)

Simplify the equation we get

⇒ \(\frac{0 \times cosx – \frac{d}{dx}cos x \times 1}{\left ( cosx \right )^{2}}\)

⇒ \(\frac{sin x}{\left ( cosx\times cosx \right )}\)

⇒ \(\left ( \frac{sin x}{cosx} \right )(\frac{1}{cosx})\)

⇒ tanx. secx

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