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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

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The solution

You have entered [src] 
   ____          
  /  2           
\/  x   - 2*x + 3
−2x+x2+3- 2 x + \sqrt{x^{2}} + 3 
  /   ____          \
d |  /  2           |
--\\/  x   - 2*x + 3/
dx
ddx(−2x+x2+3)\frac{d}{d x} \left(- 2 x + \sqrt{x^{2}} + 3\right)
Transform
Detail solution

  1. Differentiate −2x+x2+3- 2 x + \sqrt{x^{2}} + 3 term by term:

    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|}

    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: xx goes to 11

        So, the result is: 22

      So, the result is: −2-2

    5. The derivative of the constant 33 is zero.

    The result is: x∣x∣−2\frac{x}{\left|{x}\right|} - 2

The answer is:

x∣x∣−2\frac{x}{\left|{x}\right|} - 2

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     |x|
-2 + ---
      x
−2+∣x∣x-2 + \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 [√(x^2)-2x+3]
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