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Question
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Solution
\[\text{ Given }: x<2\]
\[\therefore 2-x>0\]
\[\frac{d}{dx}\left( \sqrt{x^2 - 4x + 4} \right)\]
\[ = \frac{d}{dx}\left( \sqrt{\left( 2 - x \right)^2} \right)\]
\[ = \frac{d}{dx}\left( 2 - x \right) (\because 2-x>0)\]
\[ = 0 - 1\]
\[ = - 1\]
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