Question

if y=x|x|, find dy/dx for x<0​

Answer 1

$\bigstar \underline{\underline{\sf \bf Given:-}}$

• y = x |x|
• x < 0

$\bigstar \underline{\underline{\sf \bf To\ Find:-}}$

• dy / dx .

$\bigstar \underline{\underline{\sf \bf Solution:-}}$

We know :

$\mapsto \boxed{\boxed{\sf \bold {|x|=\left \{ {{x,\ x\geq 0} \atop {-x,\ x<0}} \right. }}}$

Given , y=x|x|

For x <0, |x| = -x .

Acc to question :

$:\implies \sf y=x|x| \\\\\\:\implies \sf y=x(-x)=-x^2$

Now , Finding dy/dx :

$:\implies \sf \frac{dy}{dx} (x^2) = \underline{\bold{-2x.}}$

Hence , the Answer is -2x.

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HOPE IT HELPS !

Answer 2

Answer:

The answer is -2x ... :)