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x/sqrt(x^2-1)

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

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
     x     
-----------
   ________
  /  2     
\/  x  - 1 
$$\frac{x}{\sqrt{x^{2} - 1}}$$
d /     x     \
--|-----------|
dx|   ________|
  |  /  2     |
  \\/  x  - 1 /
$$\frac{d}{d x} \frac{x}{\sqrt{x^{2} - 1}}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    To find :

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        1. The derivative of the constant is zero.

        2. Apply the power rule: goes to

        The result is:

      The result of the chain rule is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
                    2    
     1             x     
----------- - -----------
   ________           3/2
  /  2        / 2    \   
\/  x  - 1    \x  - 1/   
$$- \frac{x^{2}}{\left(x^{2} - 1\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x^{2} - 1}}$$
The second derivative [src]
  /          2 \
  |       3*x  |
x*|-3 + -------|
  |           2|
  \     -1 + x /
----------------
           3/2  
  /      2\     
  \-1 + x /     
$$\frac{x \left(\frac{3 x^{2}}{x^{2} - 1} - 3\right)}{\left(x^{2} - 1\right)^{\frac{3}{2}}}$$
The third derivative [src]
  /                  /          2 \\
  |                2 |       5*x  ||
  |               x *|-3 + -------||
  |          2       |           2||
  |       3*x        \     -1 + x /|
3*|-1 + ------- - -----------------|
  |           2              2     |
  \     -1 + x         -1 + x      /
------------------------------------
                     3/2            
            /      2\               
            \-1 + x /               
$$\frac{3 \left(- \frac{x^{2} \cdot \left(\frac{5 x^{2}}{x^{2} - 1} - 3\right)}{x^{2} - 1} + \frac{3 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{\frac{3}{2}}}$$
The graph
Derivative of x/sqrt(x^2-1)