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Chain Rule of Differentiation

If fx = x 2+6...

Question

If $f (x) = \sqrt{x^{2} + 6 x + 9}$ , then f '(x) is equal to

A

1 f o r x > - 3

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B

- 1 f o r x < - 3

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C

1 f o r a l l x \in R

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D

0 f o r x = - 3

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Solution

The correct options are
A $1 f o r x > - 3$
B $- 1 f o r x < - 3$
$f (x) = \sqrt{x^{2} + 6 x + 9} = (x + 3 | Function is not differentiable at x = - 3 . f (x) = (\begin{matrix} - (x + 3), if x < - 3 (x + 3), if x > - 3 \end{matrix} \Rightarrow f' (x) = (\begin{matrix} - 1, if x < - 3 1, if x > - 3 \end{matrix}$

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f (x) = \sqrt{x^{2} + 6 x + 9}, then f' (x)

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