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sqrt(x^2-25)
The derivative of the function/ sqrt(x^2-25)

Derivative of sqrt(x^2-25)

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

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from to

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The solution

You have entered [src] 
   _________
  /  2      
\/  x  - 25
x2−25\sqrt{x^{2} - 25} 
sqrt(x^2 - 25)
Detail solution

  1. Let u=x2−25u = x^{2} - 25.

  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(x2−25)\frac{d}{d x} \left(x^{2} - 25\right):

    1. Differentiate x2−25x^{2} - 25 term by term:

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

      2. The derivative of the constant −25-25 is zero.

      The result is: 2x2 x

    The result of the chain rule is:

    xx2−25\frac{x}{\sqrt{x^{2} - 25}}

  4. Now simplify:

    xx2−25\frac{x}{\sqrt{x^{2} - 25}}

The answer is:

xx2−25\frac{x}{\sqrt{x^{2} - 25}}

The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     x      
------------
   _________
  /  2      
\/  x  - 25
xx2−25\frac{x}{\sqrt{x^{2} - 25}}
Simplify
The second derivative [src] 
         2   
        x    
 1 - --------
            2
     -25 + x 
-------------
   __________
  /        2 
\/  -25 + x
−x2x2−25+1x2−25\frac{- \frac{x^{2}}{x^{2} - 25} + 1}{\sqrt{x^{2} - 25}}
Simplify
The third derivative [src] 
    /         2   \
    |        x    |
3*x*|-1 + --------|
    |            2|
    \     -25 + x /
-------------------
             3/2   
   /       2\      
   \-25 + x /
3x(x2x2−25−1)(x2−25)32\frac{3 x \left(\frac{x^{2}}{x^{2} - 25} - 1\right)}{\left(x^{2} - 25\right)^{\frac{3}{2}}}
Simplify
The graph
Derivative of sqrt(x^2-25)
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