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[√(x^2)-2x+3]
The derivative of the function/ [√(x^2)-2x+3]

Derivative of [√(x^2)-2x+3]

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ____          
  /  2           
\/  x   - 2*x + 3
$$- 2 x + \sqrt{x^{2}} + 3$$ 
  /   ____          \
d |  /  2           |
--\\/  x   - 2*x + 3/
dx
$$\frac{d}{d x} \left(- 2 x + \sqrt{x^{2}} + 3\right)$$
Transform
Detail solution

  1. Differentiate term by term:

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Apply the power rule: goes to

      The result of the chain rule is:

    4. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      So, the result is:

    5. The derivative of the constant is zero.

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     |x|
-2 + ---
      x
$$-2 + \frac{\left|{x}\right|}{x}$$
Simplify
The second derivative [src] 
  |x|          
- --- + sign(x)
   x           
---------------
       x
$$\frac{\operatorname{sign}{\left(x \right)} - \frac{\left|{x}\right|}{x}}{x}$$
Simplify
The third derivative [src] 
  /|x|   sign(x)                \
2*|--- - ------- + DiracDelta(x)|
  |  2      x                   |
  \ x                           /
---------------------------------
                x
$$\frac{2 \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x} + \frac{\left|{x}\right|}{x^{2}}\right)}{x}$$
Simplify
The graph
Derivative of [√(x^2)-2x+3]
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