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The derivative of the function/ sqrt(x^2-3x-7)

Derivative of sqrt(x^2-3x-7)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ______________
  /  2           
\/  x  - 3*x - 7
$$\sqrt{\left(x^{2} - 3 x\right) - 7}$$ 
sqrt(x^2 - 3*x - 7)
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. 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. Apply the power rule: goes to

          So, the result is:

        The result is:

      2. 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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     -3/2 + x    
-----------------
   ______________
  /  2           
\/  x  - 3*x - 7
$$\frac{x - \frac{3}{2}}{\sqrt{\left(x^{2} - 3 x\right) - 7}}$$
Simplify
The second derivative [src] 
                 2   
       (-3 + 2*x)    
1 - -----------------
      /      2      \
    4*\-7 + x  - 3*x/
---------------------
     _______________ 
    /       2        
  \/  -7 + x  - 3*x
$$\frac{- \frac{\left(2 x - 3\right)^{2}}{4 \left(x^{2} - 3 x - 7\right)} + 1}{\sqrt{x^{2} - 3 x - 7}}$$
Simplify
The third derivative [src] 
  /                2 \           
  |      (-3 + 2*x)  |           
3*|-4 + -------------|*(-3 + 2*x)
  |           2      |           
  \     -7 + x  - 3*x/           
---------------------------------
                        3/2      
         /      2      \         
       8*\-7 + x  - 3*x/
$$\frac{3 \left(2 x - 3\right) \left(\frac{\left(2 x - 3\right)^{2}}{x^{2} - 3 x - 7} - 4\right)}{8 \left(x^{2} - 3 x - 7\right)^{\frac{3}{2}}}$$
Simplify
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