Question

d/dx x | x |=....... (x <0),Select Proper option from the given options.
(a) 2x
(b) -2x
(c) | x |
(d) 0

Answer 1

we have to find the value of $\frac{d}{dx}x|x|$ when x < 0.

we know, Modulus function , y = |x| is separated into two parts .
when x > 0 , y = |x| = x
when x < 0 , y = |x| = -x

similarly, here function , y = x|x|
A/c to question, x < 0 ,
so, y = x|x| = x(-x) = -x²

now, function is converted into y = -x²

so, $\frac{d}{dx}(-x^2)=-2x^{(2-1)} = -2x$

hence, option (b) is correct.