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प्रश्न
Differentiate tan 5x° ?
उत्तर
\[\text{ Let } y = \tan5x^\circ\]
\[ \Rightarrow y = \tan\left( 5x \times \frac{\pi}{180} \right)\]
\[\text{ Differentiate it with respect to x we get }, \]
\[\frac{d y}{d x} = \frac{d}{dx}\tan\left( 5x \times \frac{\pi}{180} \right)\]
\[ = \sec^2 \left( 5x \times \frac{\pi}{180} \right)\frac{d}{dx}\left( 5x \times \frac{\pi}{180} \right) \left[ \text{ using chain rule } \right]\]
\[ = \left( \frac{5\pi}{180} \right) \sec^2 \left( 5x \times \frac{\pi}{180} \right)\]
\[ = \frac{5\pi}{180} \sec^2 \left( 5x^\circ\right)\]
\[\text{Hence}, \frac{d}{dx}\left( \tan5x^\circ \right) = \frac{5\pi}{180} \sec^2 \left( 5x^\circ \right)\]
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