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sqrt(x^2-6x-11)

Derivative of sqrt(x^2-6x-11)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   _______________
  /  2            
\/  x  - 6*x - 11 
$$\sqrt{x^{2} - 6 x - 11}$$
  /   _______________\
d |  /  2            |
--\\/  x  - 6*x - 11 /
dx                    
$$\frac{d}{d x} \sqrt{x^{2} - 6 x - 11}$$
Detail solution
  1. Let .

  2. Apply the power rule: goes to

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

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. 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:

      3. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
      -3 + x      
------------------
   _______________
  /  2            
\/  x  - 6*x - 11 
$$\frac{x - 3}{\sqrt{x^{2} - 6 x - 11}}$$
The second derivative [src]
               2   
       (-3 + x)    
 1 - --------------
            2      
     -11 + x  - 6*x
-------------------
   ________________
  /        2       
\/  -11 + x  - 6*x 
$$\frac{- \frac{\left(x - 3\right)^{2}}{x^{2} - 6 x - 11} + 1}{\sqrt{x^{2} - 6 x - 11}}$$
The third derivative [src]
  /               2   \         
  |       (-3 + x)    |         
3*|-1 + --------------|*(-3 + x)
  |            2      |         
  \     -11 + x  - 6*x/         
--------------------------------
                      3/2       
      /       2      \          
      \-11 + x  - 6*x/          
$$\frac{3 \left(x - 3\right) \left(\frac{\left(x - 3\right)^{2}}{x^{2} - 6 x - 11} - 1\right)}{\left(x^{2} - 6 x - 11\right)^{\frac{3}{2}}}$$
The graph
Derivative of sqrt(x^2-6x-11)