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sqrt(x^2-x-1)
The derivative of the function/ sqrt(x^2-x-1)

Derivative of sqrt(x^2-x-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ____________
  /  2         
\/  x  - x - 1
$$\sqrt{\left(x^{2} - x\right) - 1}$$ 
sqrt(x^2 - x - 1)
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] 
    -1/2 + x   
---------------
   ____________
  /  2         
\/  x  - x - 1
$$\frac{x - \frac{1}{2}}{\sqrt{\left(x^{2} - x\right) - 1}}$$
Simplify
The second derivative [src] 
                2  
      (-1 + 2*x)   
1 - ---------------
      /      2    \
    4*\-1 + x  - x/
-------------------
     _____________ 
    /       2      
  \/  -1 + x  - x
$$\frac{- \frac{\left(2 x - 1\right)^{2}}{4 \left(x^{2} - x - 1\right)} + 1}{\sqrt{x^{2} - x - 1}}$$
Simplify
The third derivative [src] 
             /               2\
             |     (-1 + 2*x) |
3*(-1 + 2*x)*|-4 + -----------|
             |           2    |
             \     -1 + x  - x/
-------------------------------
                      3/2      
         /      2    \         
       8*\-1 + x  - x/
$$\frac{3 \left(2 x - 1\right) \left(\frac{\left(2 x - 1\right)^{2}}{x^{2} - x - 1} - 4\right)}{8 \left(x^{2} - x - 1\right)^{\frac{3}{2}}}$$
Simplify
The graph
Derivative of sqrt(x^2-x-1)
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