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| $
Show Answer
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| $ .