Questions

What Is The Derivative Of tan(x)?

Derivative of \(tanx = sec^2x \)

What Is The Derivative Of tan(x)?

\( \frac{d}{dx} {tanx} = \frac{d}{dx} \frac{sinx}{cosx}\) [we know that \( tanx =\frac{sinx}{cosx} \)]

\( => \frac{d}{dx} {tanx} = \frac{cosx \times \frac{d}{dx} {sinx} – \frac{d}{dx} {cosx} \times sinx}{cos^2x} \) [Use Quotient Rule]

\( => \frac{d}{dx} {tanx} = \frac{cosx \times cosx – (-sinx) \times sinx}{cos^2x} \) [Simply]

\( => \frac{d}{dx} {tanx} = \frac{cos^2x + sin^2x }{cos^2x} \)

Use the Pythagorean identity for sine and cosine [\( sin^2x + cos^2x =1 \)]

\( => \frac{d}{dx} {tanx} = \frac{1 }{cos^2x} \)

we know that \( \frac{1}{cosx} =secx \)

\( => \frac{d}{dx} {tanx} = sec^2x \)