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Derivative of:
Derivative of x^3*atan(x)
Derivative of -((x^2+196)/x)
Derivative of (x-1)*e^x
Derivative of sqrt(x^2-6*x+13)
Identical expressions
sqrt(x^ two - six *x+ thirteen)
square root of (x squared minus 6 multiply by x plus 13)
square root of (x to the power of two minus six multiply by x plus thirteen)
√(x^2-6*x+13)
sqrt(x2-6*x+13)
sqrtx2-6*x+13
sqrt(x²-6*x+13)
sqrt(x to the power of 2-6*x+13)
sqrt(x^2-6x+13)
sqrt(x2-6x+13)
sqrtx2-6x+13
sqrtx^2-6x+13
Similar expressions
sqrt(x^2-6*x-13)
sqrt(x^2+6*x+13)

The derivative of the function/ sqrt(x^2-6*x+13)

Derivative of sqrt(x^2-6*x+13)

The solution

You have entered [src]

   _______________
  /  2            
\/  x  - 6*x + 13

$$\sqrt{\left(x^{2} - 6 x\right) + 13}$$

sqrt(x^2 - 6*x + 13)

Detail solution

Let $u = \left(x^{2} - 6 x\right) + 13$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\left(x^{2} - 6 x\right) + 13\right)$ :
1. Differentiate $\left(x^{2} - 6 x\right) + 13$ term by term:
  1. Differentiate $x^{2} - 6 x$ term by term:
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    2. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $-6$
    The result is: $2 x - 6$
  2. The derivative of the constant $13$ is zero.
  The result is: $2 x - 6$
The result of the chain rule is:

$\frac{2 x - 6}{2 \sqrt{\left(x^{2} - 6 x\right) + 13}}$
Now simplify:

$\frac{x - 3}{\sqrt{x^{2} - 6 x + 13}}$

The answer is:

$\frac{x - 3}{\sqrt{x^{2} - 6 x + 13}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      -3 + x      
------------------
   _______________
  /  2            
\/  x  - 6*x + 13

$$\frac{x - 3}{\sqrt{\left(x^{2} - 6 x\right) + 13}}$$

Simplify

The second derivative [src]

              2   
      (-3 + x)    
1 - ------------- 
          2       
    13 + x  - 6*x 
------------------
   _______________
  /       2       
\/  13 + x  - 6*x

$$\frac{- \frac{\left(x - 3\right)^{2}}{x^{2} - 6 x + 13} + 1}{\sqrt{x^{2} - 6 x + 13}}$$

Simplify

The third derivative [src]

  /               2  \         
  |       (-3 + x)   |         
3*|-1 + -------------|*(-3 + x)
  |           2      |         
  \     13 + x  - 6*x/         
-------------------------------
                      3/2      
       /      2      \         
       \13 + x  - 6*x/

$$\frac{3 \left(x - 3\right) \left(\frac{\left(x - 3\right)^{2}}{x^{2} - 6 x + 13} - 1\right)}{\left(x^{2} - 6 x + 13\right)^{\frac{3}{2}}}$$

Simplify

The graph

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Derivative of sqrt(x^2-6*x+13)

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The solution