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sqrt(x^2-12x+56)

Derivative of sqrt(x^2-12x+56)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   ________________
  /  2             
\/  x  - 12*x + 56 
$$\sqrt{x^{2} - 12 x + 56}$$
  /   ________________\
d |  /  2             |
--\\/  x  - 12*x + 56 /
dx                     
$$\frac{d}{d x} \sqrt{x^{2} - 12 x + 56}$$
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]
       -6 + x      
-------------------
   ________________
  /  2             
\/  x  - 12*x + 56 
$$\frac{x - 6}{\sqrt{x^{2} - 12 x + 56}}$$
The second derivative [src]
               2   
       (-6 + x)    
 1 - --------------
           2       
     56 + x  - 12*x
-------------------
   ________________
  /       2        
\/  56 + x  - 12*x 
$$\frac{- \frac{\left(x - 6\right)^{2}}{x^{2} - 12 x + 56} + 1}{\sqrt{x^{2} - 12 x + 56}}$$
The third derivative [src]
  /               2   \         
  |       (-6 + x)    |         
3*|-1 + --------------|*(-6 + x)
  |           2       |         
  \     56 + x  - 12*x/         
--------------------------------
                      3/2       
      /      2       \          
      \56 + x  - 12*x/          
$$\frac{3 \left(x - 6\right) \left(\frac{\left(x - 6\right)^{2}}{x^{2} - 12 x + 56} - 1\right)}{\left(x^{2} - 12 x + 56\right)^{\frac{3}{2}}}$$
The graph
Derivative of sqrt(x^2-12x+56)