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

Derivative of sqrt(x^2-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ________
  /  2     
\/  x  - 1
$$\sqrt{x^{2} - 1}$$ 
sqrt(x^2 - 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. Apply the power rule: goes to

      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] 
     x     
-----------
   ________
  /  2     
\/  x  - 1
$$\frac{x}{\sqrt{x^{2} - 1}}$$
Simplify
The second derivative [src] 
        2   
       x    
1 - ------- 
          2 
    -1 + x  
------------
   _________
  /       2 
\/  -1 + x
$$\frac{- \frac{x^{2}}{x^{2} - 1} + 1}{\sqrt{x^{2} - 1}}$$
Simplify
The third derivative [src] 
    /         2  \
    |        x   |
3*x*|-1 + -------|
    |           2|
    \     -1 + x /
------------------
            3/2   
   /      2\      
   \-1 + x /
$$\frac{3 x \left(\frac{x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{\frac{3}{2}}}$$
Simplify
The graph
Derivative of sqrt(x^2-1)
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