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Derivative of:
Derivative of (x-2)^3
Derivative of sqrt(x^2-1)
Derivative of ln(x)/x
Derivative of ln(x^2+1)
Integral of d{x}:
sqrt(x^2-1)
Graphing y =:
sqrt(x^2-1)
Identical expressions
sqrt(x^ two - one)
square root of (x squared minus 1)
square root of (x to the power of two minus one)
√(x^2-1)
sqrt(x2-1)
sqrtx2-1
sqrt(x²-1)
sqrt(x to the power of 2-1)
sqrtx^2-1
Similar expressions
sqrt(x^2+1)
y(x)=x/sqrtx^2-1
atan(x)*sqrt(x^2-1)

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

Derivative of sqrt(x^2-1)

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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Identical expressions

Similar expressions

Derivative of sqrt(x^2-1)

The graph:

Piecewise:

The solution