Question

Differentiate tan 5x° ?

Answer 1

\[\text{ Let } y = \tan5x^\circ\]

\[ \Rightarrow y = \tan\left( 5x \times \frac{\pi}{180} \right)\]

\[\text{ Differentiate it with respect to x we get }, \]

\[\frac{d y}{d x} = \frac{d}{dx}\tan\left( 5x \times \frac{\pi}{180} \right)\]

\[ = \sec^2 \left( 5x \times \frac{\pi}{180} \right)\frac{d}{dx}\left( 5x \times \frac{\pi}{180} \right) \left[ \text{ using chain rule } \right]\]

\[ = \left( \frac{5\pi}{180} \right) \sec^2 \left( 5x \times \frac{\pi}{180} \right)\]

\[ = \frac{5\pi}{180} \sec^2 \left( 5x^\circ\right)\]

\[\text{Hence}, \frac{d}{dx}\left( \tan5x^\circ \right) = \frac{5\pi}{180} \sec^2 \left( 5x^\circ \right)\]