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sqrt(x^2-25)

Derivative of sqrt(x^2-25)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   _________
  /  2      
\/  x  - 25 
$$\sqrt{x^{2} - 25}$$
sqrt(x^2 - 25)
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
The first derivative [src]
     x      
------------
   _________
  /  2      
\/  x  - 25 
$$\frac{x}{\sqrt{x^{2} - 25}}$$
The second derivative [src]
         2   
        x    
 1 - --------
            2
     -25 + x 
-------------
   __________
  /        2 
\/  -25 + x  
$$\frac{- \frac{x^{2}}{x^{2} - 25} + 1}{\sqrt{x^{2} - 25}}$$
The third derivative [src]
    /         2   \
    |        x    |
3*x*|-1 + --------|
    |            2|
    \     -25 + x /
-------------------
             3/2   
   /       2\      
   \-25 + x /      
$$\frac{3 x \left(\frac{x^{2}}{x^{2} - 25} - 1\right)}{\left(x^{2} - 25\right)^{\frac{3}{2}}}$$
The graph
Derivative of sqrt(x^2-25)