Differentiation Question 200

Question: The derivative of $ f(x)=x|x| $ is

[SCRA 1996]

Options:

A) $ 2x $

B) - 2x

C) $ 2x^{2} $

D) $ 2|x| $

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Answer:

Correct Answer: D

Solution:

$ f(x)= \begin{cases} & -x^{2},\ x<0 \\ & x^{2}\ \ ,\ x>0 \\ \end{cases} .\Rightarrow f’(x)= \begin{cases} & -2x,x<0 \\ & 2x,x>0 \\ \end{cases} . $

$ \therefore f’(x)=2|x| $ .