Differentiate the function with respect to $x$
$sin (a x + b)$

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Solution

Let $y = sin (a x + b)$
Thus using chain rule,
$\frac{d y}{d x} = \frac{d (sin (a x + b))}{d (a x + b)} \cdot \frac{d (a x + b)}{d x} = a cos (a x + b)$

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