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Circular Measurement of Angle

If fx=x. | ...

Question

If $f (x) = x . | x |$ , then its derivative is:

A

2 x

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B

- 2 x

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C

2 | x |

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D

2 x s g n x

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Solution

The correct options are
C $2 | x |$
D $2 x s g n x$
$x | x | = x . \sqrt{x^{2}}$
Its derivative will be,
$= \frac{x^{2}}{\sqrt{x^{2}}} + \sqrt{x^{2}}$
$= \frac{2 x^{2}}{\sqrt{x^{2}}}$
$= 2 | x |$

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