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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
x2−1\sqrt{x^{2} - 1} 
sqrt(x^2 - 1)
Detail solution

  1. Let u=x2−1u = x^{2} - 1.

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

  3. Then, apply the chain rule. Multiply by ddx(x2−1)\frac{d}{d x} \left(x^{2} - 1\right):

    1. Differentiate x2−1x^{2} - 1 term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      2. The derivative of the constant −1-1 is zero.

      The result is: 2x2 x

    The result of the chain rule is:

    xx2−1\frac{x}{\sqrt{x^{2} - 1}}

  4. Now simplify:

    xx2−1\frac{x}{\sqrt{x^{2} - 1}}

The answer is:

xx2−1\frac{x}{\sqrt{x^{2} - 1}}

The graph
02468-8-6-4-2-101020-10
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     x     
-----------
   ________
  /  2     
\/  x  - 1
xx2−1\frac{x}{\sqrt{x^{2} - 1}}
Simplify
The second derivative [src] 
        2   
       x    
1 - ------- 
          2 
    -1 + x  
------------
   _________
  /       2 
\/  -1 + x
−x2x2−1+1x2−1\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 /
3x(x2x2−1−1)(x2−1)32\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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