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Derivative of:
Derivative of -e^x
Derivative of 1/2*sqrt(x)
Derivative of x-7
Derivative of x^5-5*x^3-20*x
Graphing y =:
(x^2-1)^(1/2)
Integral of d{x}:
(x^2-1)^(1/2)
Identical expressions
(x^ two - one)^(one / two)
(x squared minus 1) to the power of (1 divide by 2)
(x to the power of two minus one) to the power of (one divide by two)
(x2-1)(1/2)
x2-11/2
(x²-1)^(1/2)
(x to the power of 2-1) to the power of (1/2)
x^2-1^1/2
(x^2-1)^(1 divide by 2)
Similar expressions
(x^2+1)^(1/2)

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

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

The solution

You have entered [src]

   ________
  /  2     
\/  x  - 1

$$\sqrt{x^{2} - 1}$$

sqrt(x^2 - 1)

Detail solution

Let $u = x^{2} - 1$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 1\right)$ :
1. Differentiate $x^{2} - 1$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $-1$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$\frac{x}{\sqrt{x^{2} - 1}}$
Now simplify:

$\frac{x}{\sqrt{x^{2} - 1}}$

The answer is:

$\frac{x}{\sqrt{x^{2} - 1}}$

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

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

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The solution