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If f(x)=x|x|, then prove that f^(prime)(...

If `f(x)=x|x|,` then prove that `f^(prime)(x)=2|x|`

Text Solution

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`f(x)=x|x|, ne 0`
`rArr" "f(x)={:{(-x^(2), x lt 0),(x^(2), x gt 0):}`
`rArr" "f'(x)={:{(-2"x,","" x lt 0),(2"x,",""x gt 0):}`
`therefore" "f'(x)=2|x|, x ne 0`
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