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Question
(ax + b) (a + d)2
Solution
\[(ax + b)(a + d )^2 \]
\[\text{ Let } u = ax + b, v = \left( a + d \right)^2 \]
\[\text{ Then }, u' = a, v' = 0\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = u v' + v u'\]
\[\frac{d}{dx}\left( (ax + b)(a + d )^2 \right) = (ax + b) \times 0 + \left( a + d \right)^2 \times a\]
\[ \therefore \frac{d}{dx}\left( (ax + b)(a + d )^2 \right) = a \left( a + d \right)^2\]
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