If x<2, then write the value of d dx ( x^2-4x+4 ) - Vidyadip

Question

If x<2, then write the value of $\frac{\text{d}}{\text{dx}}(\sqrt{\text{x}^2-\text{4x}+4})$

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Answer

$\frac{\text{d}}{\text{dx}}(\sqrt{\text{x}^2-\text{4x}+4})=\frac{\text{d}}{\text{dx}}\Big(\sqrt{(\text{x}-2)^2}\Big)$

$=\frac{\text{d}}{\text{dx}}(|\text{x}-2|)$

$=\frac{\text{d}}{\text{dx}}(-(\text{x}-2))\ (\because\text{x}<2)$

$=-1$

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