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sqrt(x^2)
The derivative of the function/ sqrt(x^2)

Derivative of sqrt(x^2)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ____
  /  2 
\/  x
x2\sqrt{x^{2}} 
  /   ____\
d |  /  2 |
--\\/  x  /
dx
ddxx2\frac{d}{d x} \sqrt{x^{2}}
Transform
Detail solution

  1. Let u=x2u = x^{2}.

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

  3. Then, apply the chain rule. Multiply by ddxx2\frac{d}{d x} x^{2}:

    1. Apply the power rule: x2x^{2} goes to 2x2 x

    The result of the chain rule is:

    x∣x∣\frac{x}{\left|{x}\right|}

The answer is:

x∣x∣\frac{x}{\left|{x}\right|}

The graph
02468-8-6-4-2-101020-10
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
|x|
---
 x
∣x∣x\frac{\left|{x}\right|}{x}
Simplify
The second derivative [src] 
  |x|          
- --- + sign(x)
   x           
---------------
       x
sign⁡(x)−∣x∣xx\frac{\operatorname{sign}{\left(x \right)} - \frac{\left|{x}\right|}{x}}{x}
Simplify
The third derivative [src] 
  /|x|   sign(x)                \
2*|--- - ------- + DiracDelta(x)|
  |  2      x                   |
  \ x                           /
---------------------------------
                x
2(δ(x)−sign⁡(x)x+∣x∣x2)x\frac{2 \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x} + \frac{\left|{x}\right|}{x^{2}}\right)}{x}
Simplify
The graph
Derivative of sqrt(x^2)
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