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Question
Differentiate sin (3x + 5) ?
Solution
\[\text{ Let } y = \sin\left( 3x + 5 \right)\]
\[\text{ Differentiating y with respect to x we get }, \]
\[\frac{d y}{d x} = \frac{d}{dx}\sin\left( 3x + 5 \right)\]
\[ = \cos\left( 3x + 5 \right)\frac{d}{dx}\left( 3x + 5 \right) \left[ \text{ using chain rule } \right]\]
\[ = \cos\left( 3x + 5 \right) \times 3\]
\[ = 3\cos\left( 3x + 5 \right)\]
\[So, \frac{d}{dx}\left\{ \sin\left( 3x + 5 \right) \right\} = 3\cos\left( 3x + 5 \right)\]
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